It’s impossible to prove a negative, but I’m going to say that I have never seen such an option, and it seems unlikely given Wizards’ design for them to make a generic option along these lines. A feat specific to a certain race or creature, sure: then you can know exactly what it is you’re offering. But if the feat or whatever is generic, then the authors of the feat have no idea just how much DR they’re improving, and they may possibly be unaware how much they are improving it.
For example, if the feat were so broad as to apply to any amount of any type of DR, and add an additional restriction of “-and-slashing” to it, a lich’s DR goes from 15/bludgeoning-and-magic to 15/bludgeoning-and-magic-and-slashing, sharply limiting the number of weapons that can actually bypass it (executioner’s mace from Dungeon vol. 135 is the only wieldable weapon in the entire game that could do it; bite attacks could also). The lich’s DR was always good; this makes it basically perfect.
Potentially worse, though, is someone who had just DR/magic, since usually DR/magic is close to meaningless. Making that DR/magic-and-slashing makes it much more significant. Since DR/magic is close to meaningless, designers are often comfortable putting far larger numbers before than slash than for other forms of DR. Such a feat turns that overly-large number into something very meaningful, and that’s a big deal.
Finally, Wizards was always (overly, really) conservative with DR for players. Since there were relatively few feats written just for the DM, and feats were often seen as a “player thing,” it would be out of character for them to write a particularly flexible DR-changing feat.
Considering all of this, and my rather-extensive knowledge of the options available in 3.5, I’m going to say this doesn’t exist in the general case. There may be options for, say, a shifter or warforged or something specific like that, but not just a general use one. Additionally, lycanthropes never saw very much support, so I tend to doubt there is one just for them. For the sake of double-checking, though, I have looked through the Savage Species feats, as Savage Species is by far the most likely book to find this kind of thing; it does not.
DR is deducted per hit, not per die.
Flurry of Blows suffers a deduction to each successful hit. Each attack's damage roll is totaled up separately from each other, and DR is applied to each separately. If a Monk hits with 3 attacks out of 7, then the DR applies three times, once to each individual damage roll total.
DR from multiple sources do not stack.
On a per attack level, you simply apply the strongest source of DR.
Relevant Damage Reduction Ruling
If a creature has damage reduction from more than one source, the two forms of damage reduction do not stack. Instead, the creature gets the benefit of the best damage reduction in a given situation.
If you make multiple attacks of different damage types per round (deciding to slash instead of pierce with a weapon at the end of a full attack), then the best DR source may be different for each attack.
Certain damages bypasses DR
Energy damage (such as Fire), Damage from Spells, and Damage from Supernatural Abilities will generally not be reduced by DR unless otherwise stated.
Generally, the sources of damage reduced by damage reduction are Slashing, Piercing, Blunt, and untyped physical damage (such as that from from falling).
DR/X or DR/-
This format may be confusing. Instead of this DR applying to the damage type X, it applies to everything else. This was not directly asked by the asker, but it's important to address to someone who's not familiar with the DR system.
DR vs. Slashing/Piercing/Blunt/etc.
Each type of damage dealt by an attack is separated into totals for each type/element. The defender's best DR is chosen and deducted from the relevant totals.
If any damage type is reduced to 0 damage, DR has no further effect on that damage type. For example, if only part of your damage is piercing, but the piercing DR would reduce that piercing damage to below 0, it instead reduces it to 0. If this would reduce all damage dealt by an attack to 0 total damage, the damage is ignored altogether as well as most special effects that accompany the attack, such as injury poison, a monk's stunning, and injury-based disease.
Putting it all together
Dealing +1d6 Piercing +1d6 Fire with a +4 STR bonus flurrying for 4 times against a DR 1/Slashing, 3 DR vs. Piercing, 1 DR vs. Slashing:
The best DR source the defender has for each attack is 3 DR vs. Piercing, so it is applied.
1d6+1 P +1d6 Fire
1d6+1 P +1d6 Fire
1d6+1 P +1d6 Fire
1d6+1 P +1d6 Fire
Best Answer
A crushing wall trap doesn't require an attack roll (2000 DMG 115) and neither does the compacting room (2003 & 2012 DMG 72)—and there's no provision in either DMG for stapling spikes on the wall to make either traps nastier— and while the DM makes attack rolls for a spiked pit trap (20 ft. deep) (2000 DMG 115) and a spiked pit trap (2003 & 2012 DMG 72), these aren't normal attacks. Further examples are necessary even to have a question because…
DR Only Affects Damage from Weapons and Natural Attacks
A hero can kill a creature he can't damage with his weapon by luring it into a nasty enough trap, and a creature with up to 6 hp and DR 5/magic can be killed by an unlucky fall.
Damage reduction hasn't affected anything but damage from weapons and natural attacks in Dungeons and Dragons, 3rd Edition (2000) and Dungeons and Dragons 3.5 (2003). This means most traps (except those employing weapons, which some do) will automatically overcome a creature's damage reduction.
Therefore unless the trap's an actual weapon or natural attack, DR doesn't apply. Moving walls (unless your poor PC is being beaten by a creature using a wall as an improvised weapon) and falls will bypass DR. The spikes at the pit's bottom are the DM's call (cf. armor spikes/spiked armor), however. (Don't forget to totally swoop on them, Grayhawk style, if the DM is putting +1 spikes at the bottom of pit traps just to overcome a PC's damage reduction; you earned those!)
"Why Would Damage Reduction Work This Way?"
I don't know. Seriously. I'll happily speculate, though. Although I'm unfamiliar with earlier editions of Dungeons and Dragons, in at least Advanced Dungeons and Dragons and Advanced Dungeons and Dragons, Second Edition some creatures were flat-out, straight-up immune to weapons if the weapon didn't have a sufficient magical plus (e.g. Advanced Dungeons and Dragons has in its Monster Manual the vampire, which has the entry Special Defenses: +1 or better weapons to hit (99); Advanced Dungeons and Dragons, 2nd Edition has in its Monstrous Manual the pit fiend, which has the entry Special Defenses: +3 or better weapons to hit (11)).
This led to the phrase You must be this tall to play; that is, a party must possess sufficient magical equipment (which was much rarer in earlier editions) to combat a particular monster else the party, upon encountering the monster, fought it with magic spells (which were much more constrained in earlier editions), parleyed (not usually to the party's benefit), fled, used their combined ingenuity, were granted an out by the DM, or just died. Since all but the first were… distasteful, and the first unavailable to many characters, the concept of +X or better weapons to hit was changed to damage reduction in Dungeons and Dragons, 3rd Edition, which let combat ensue even against monsters who would've formerly been invulnerable to the party's warriors' attacks, albeit at a disadvantage if the party's warriors lacked the proper gear.
With that in mind, damage reduction wasn't ever intended to be a panacea against damage in general and was instead developed as a legacy to evoke older editions which had monsters that could only be hit by +X or better weapons, and weapons only and specifically. So, yeah, my guess is that falls and traps kill monsters with damage reduction in Dungeons and Dragons, 3rd Edition and its update because those killed monsters in older editions, too.
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A Comparison of DR in Dungeons and Dragons, 3rd Edition (2000) and Dungeons and Dragons 3.5 (2003, 2012)
Although tagged as a Dungeons and Dragons, 3rd Edition question, it's useful to know these rules aren't edition-specific.
The Player's Handbook
The two big deals for damage reduction in both editions of the Player's Handbook are the barbarian's damage reduction and the damage reduction granted by the spell stoneskin.
The Player's Handbook (2000) describes the barbarian's damage reduction as
The Player's Handbook (2003, 2012) describes the barbarian's damage reduction almost identically, except it clarifies further: The barbarian
Further, the Player's Handbook (2000) contains the 4th-level Sor/Wiz spell stoneskin [abjur] (257), which reads
And the Player's Handbook (2003, 2012) describes the spell stoneskin almost identically, except it clarifies further:
Emphasis in quotations mine.
The difference here, then, between damage reduction in Player's Handbooks for Dungeons and Dragons, 3rd Edition and Dungeons and Dragons, 3.5 is that—y'know, obviously, apart from how damage reduction works—is that when using the Player's Handbook (2003, 2012) one no longer needs to look for confirmation in the Dungeon Master's Guide or Monster Manual to determine absolutely that damage reduction only works against weapons, even though that was very strongly implied by the Player's Handbook (2000), as shown by the emphasized text.
The Dungeon Master's Guide
Although it received the most serious overhaul during the Dungeons and Dragons, 3rd Edition transition to Dungeons and Dragons 3.5, the description of damage reduction in the Special Abilities section of the Dungeon Master's Guide (2000) reads
and the Dungeon Master's Guide (2003, 2012) reads
Emphasis mine. The remainder of descriptions of damage reduction in the Dungeon Master's Guides is how damage reduction's overcome by weapons (or "normal attacks") and natural attacks.
The Monster Manual
The Monster Manual doesn't say damage reduction applies to anything but weapons and natural attack either.
According to the Monster Manual (2000) damage reduction means
The Monster Manual (2003, 2012) is almost identical, saying that damage reduction means
Emphasis mine.
And then the Monster Manual (2000) describe how damage reduction is overcome by magic weapons with different bonuses, weapons composed of different materials, and certain types of creatures, while the Monster Manual (2003, 2012) describes how damage reduction is overcome by weapons composed of different materials and certain types of creatures. Because while what overcomes damage reduction changed between Dungeons and Dragons, 3rd Edition and Dungeons and Dragons 3.5, nothing changed about damage reduction itself.
Possible Contentions & Other Sources
A bone can be picked with the phrase normal attack, which is used instead of weapon or natural attack in some discussions of damage reduction, and that is somewhat problematic (e.g. in the Dungeon Master's Guide (2003, 2012), the CR 2 trap spiked pit trap (71) has spikes that get an attack roll, the CR 4 trap collapsing column (DMG 72) gets an attack roll), but I think that it's possible to agree that falling into a spiked pit or being crushed by collapsing column, for example, isn't a normal attack.
Another can be picked—for several reasons—with the frequent, ill-advised, and formally undefined use of the word blow. Dungeons and Dragons, 3rd Edition and Dungeons and Dragons 3.5 commonly and most frequently uses blow to mean an attack from a weapon or natural attack. Restrain your inner 12-year-old while I list feats like Awesome Blow (2003, 2012 MM 303), Death Blow (SF 6), Low Blow (Rac 166), Telling Blow (PH2 83), and—undoubtedly present due to lax editorial oversight and renamed by any player whose character took it—Toothed Blow (Sto 94); the 9th-level Tiger Claw martial maneuver feral death blow [strike] (ToB 87) and the 5th-level Diamond Mind martial maneuver disrupting blow [strike] (ToB 63); and even the 3rd-level Sor/Wiz spell dolorous blow [trans] (SpC 70). All of these involve weapon attacks or attacks with natural weapons.
Saying the SRD is incomplete and lacks context about this issue is a little unfair. The SRD omits only the examples from the Monster Manual (2003, 2012) for damage reduction, and all of those Monster Manual examples mention weapons or natural attacks, and, in fact, seem to be very careful to do so.
Finally, damage reduction is far more vague in Pathfinder, with its change to damage reduction's language, but that's beyond this question's scope.