Unless a magic weapon special ability says so, a weapon special ability isn't bestowed upon a weapon's ammunition

Magic items—like feats, spells, and other effects—do only what they say they do unless the DM says otherwise. Thus if a weapon special ability does not say that the weapon special ability is bestowed upon its ammunition, the weapon with that weapon special ability does not bestow that weapon special ability upon its ammunition.

However, that doesn't prevent the existence of weapons like the +1 dancing longbow, the +1 wounding crossbow, or the +1 spell storing sling, but those weapon special abilities when applied to those weapons apply only to the weapons themselves rather than to the ammunition they launch; usually this means if wielders want those special abilities to take effect the weapons must be used as improvised weapons (PH 113).

Addressing these examples, a loosed +1 dancing longbow smacks folks on its own as if the wielder were using it as an improvised weapon, a wizard who successfully bashes a bear with his +1 wounding crossbow does so using the crossbow as an improvised weapon but nonetheless magically wounds the bear, and when the halfling outrider slaps his mount with his +1 spell storing sling the outrider can take a free action to cast on his mount the spell stored within that sling. (Slapping even an allied creature with a +1 spell storing sling is still using the sling as an improvised weapon.)

The Dungeon Master's Guide's tables don't tell the whole story

When making a case for limiting weapon special abilities to certain weapons, proponents often point to Table 7–14: Melee Weapon Special Abilities and Table 7–15: Ranged Weapon Special Abilities and say that if a weapon special ability doesn't appear on the appropriate table that weapon special ability can't be placed on weapons of that type. However, the reason these tables are present is for

Random Generation: To generate magic weapons randomly, first roll on Table 7–9: Weapons, and then roll on Table 7–10: Weapon Type Determination. Use Table 7–14: Melee Weapon Special Abilities, Table 7–15: Ranged Weapon Special Abilities, or Table 7–16: Specific Weapons if indicated by the roll on Table 7–9. (DMG 223)

So if not generating magic weapons randomly, the tables go unused.

What the tables are actually doing is preventing the DM from being a jerk. See, when the DM is randomly generating a creature's treasure, he rolls on Table 7–9: Weapons to determine the weapon's enhancement bonus, then on Table 7–10: Weapon Type Determination (yielding a 70% chance of a melee weapon, 20% chance of a ranged weapon, and a 10% chance of an uncommon weapon); then on the kind-of-weapon Tables 7–11, 7–12, or 7–13; then, finally, on the appropriate melee weapon special ability or ranged weapon special ability table (Table 7–14 or 7–15). Because Table 7–13: Common Ranged Weapons includes both ammunition and the weapons using ammunition, every weapon special ability on Table 7–15: Ranged Weapon Special Abilities must be compatible with both ranged weapons and their ammunition.¹

Were there but a lone table for randomly determining weapon special abilities, the DM would either roll until getting an effective combination or laugh maniacally as he generated stupid weapons suitable only as vendor trash. For example, the tables prevent the DM from randomly generating loot piles containing +1 disruption longbows (which unleash their destructive power against undead when such longbows are used as improvised weapons) or +1 speed arrows (which give an extra attack when used as improvised weapons). The tables for random treasure generation are actually kind of spiffy that way.²

Curious Case #1: Defending

The weapon special ability defending says

A defending weapon allows the wielder to transfer some or all of the sword’s enhancement bonus to his AC as a bonus that stacks with all others. As a free action, the wielder chooses how to allocate the weapon’s enhancement bonus at the start of his turn before using the weapon, and the effect to AC lasts until his next turn. (DMG 224)

Emphasis mine. Other defending weapons notwithstanding (e.g. the dagger of defense (AE 104) (58,302 gp; 1 lb.); the dwarven waraxe Gharriakha, the Hearthwarden (RS 165) (61,830 gp; 8 lbs.)), the defending weapon special ability is, according to the rules as written, limited to swords, and has been so limited throughout the entirety of Dungeons and Dragons, Third Edition, including in the premium edition Dungeon Master's Guide (2013).

Curious Case #2: Spell storing

The most contentious of weapon special abilities, the weapon special ability spell storing says that

Any time the weapon strikes a creature and the creature takes damage from it, the weapon can immediately cast the spell on that creature as a free action if the wielder desires. (DMG 225)

Emphasis mine. Thus the DM must determine if ammunition and thrown weapons, after being loosed, are still wielded. You can read more about the controversy surrounding the weapon special ability spell storing in these threads from 2002, 2006, 2008, 2012, and also 2012.

The tables for randomly generating treasure don't prevent DMs from placing (rather than randomly generating) appropriate magic weapons nor do the tables prevent the PCs from creating appropriate magic weapons. For example, +1 keen crossbow bolts and +1 disruption sling bullets are equally legit, as are usually dumb weapons like the aforementioned +1 dancing longbow et al.

To avoid arguments, put magic weapon special abilities in the format used by the Magic Item Compendium

Prior to the Magic Item Compendium (Mar. 2007) magic weapon special abilities were not, as part of their typical descriptions, called out as limited to either ammunition, melee weapons, ranged weapons, or a combination of these. Authors and editors were relied upon to remember to have weapon special abilities apply to appropriate weapons. This sometimes led to omissions, mistakes, and strangeness. For example, the weapon special ability smoking (+1 bonus) (Lords of Darkness 180), as written, can be applied to any weapon but is potentially unbalancing and probably changes the DM's view of his setting significantly when every character who can afford one wields a +1 smoking crossbow bolt (166 gp 1 sp; 0.1 lbs.).

After the Magic Item Compendium, a weapon special ability's description includes the entry Property which specifies the type of item to which the weapon special ability can be applied (e.g. ammunition, melee weapon, weapon).³ (A similar history applies to armor and shield special abilities.) But, as Dungeons and Dragons 3.5 ceased publication only about a year after the Magic Item Compendium, this leaves the vast majority of weapon special abilities unspecified as to what they can be applied except in their description.

I suggest that if you've a particular weapon special ability you want to use dating from before the Magic Item Compendium you put it in a format similar to the Magic Item Compendium's and submit it to the DM for review. He'll appreciate you doing the extra work, and, after it's approved, you and he can really be on the same page as to how and on what it functions.

¹ The DMG implies that ammunition are weapons; if not, the only weapon special ability available for ammunition is brilliant energy (DMG 224).
² Random generation doesn't wholly prevent stupid weapons. For example, the DM can still roll a +5 brilliant energy returning net.
³ For comparison, Dungeonscape (Feb. 2007) contains the weapon special ability swarmstrike (+1 bonus) (Du 40), which is unclear as to whether swarmstrike ranged weapons bestow that special ability on their ammunition, implying they do but never stating so, but Drow of the Underdark (May 2007) has several magic weapon special abilities, all of which are clear as to what they can be applied and when a ranged weapon bestows the special ability on its ammunition.

If we assume that all spells and items at your disposal restore your health by regaining hit points, and we also assume that all the damage dealt to our hypothetical character was dealt by the Sword of Wounding, it would seem that the character is eternally stuck at 0 HP.

However, let us turn to the "Recuperating" downtime activity listed on page 187 of the PHB (emphasis mine):

You can use downtime between adventures to recover from debilitating injury, disease, or poison.

After three days of downtime spent recuperating, you can make a DC 15 Constitution saving throw. On a successful save, you can choose one of the following results:

• End one effect on you that prevents you from regaining hit points.
• For the next 24 hours, gain advantage on saving throws against one disease or poison currently affecting you.

So, after 3 days you can make a DC 15 Con save to try and remove the effect of the Sword of Wounding from your character. If you fail, you can try again in another 3 days, provided that your unconscious body is actually allowed to have downtime to recuperate (i.e. left to rest somewhere in a bed, while the rest of the party does their own downtime activities). Once you have made the save, you are both:

• stable at 0 HP, and
• able to regain hit points again, meaning that in 1d4 hours you will be back up with 1 hit point (or sooner with potentially more HP if you receive healing).