[RPG] What happens if you sequester a target which has a spell with a duration running on it

Short answer: The rules don't say. Choose whatever you consider coolest.

Somewhat longer answer:

I would expect yes. Effects are said to travel with their subjects, so they can explicitly exceed for example their range once they've been cast. An effect with a non-concentration duration is therefore a feature of the subject and should share its frame of reference. You obviously can't actually issue commands to the subject while it's in stasis.

That's my expectation, but I think the real answer depends on how you conceptualize temporal stasis. Ask yourself this: Can a subject of temporal stasis be stripped of its gear? Neither the spell nor the rules governing targeting specify, but I consider the answer to be "no". And I construe an ongoing spell effect as just another thing that is temporarily part of the subject, but that's not the only valid interpretation of events.

Note: This DM wouldn't have temporal stasis cast on the recently dead wizard but have his followers and acolytes immediately slather him in unguent of timelessness. If the idiosyncrasies of bringing back the dead in dnd-3.5e don't interest you, skip to the section Besides maybe temporal stasis, what other means can preserve a dead creature for 3,000 years? as subquestions are answered in the order they appear in the question.

Can the caster of temporal stasis target a dead creature with the spell?

Ask the DM. However, this DM believes it's possible despite the FAQ ruling that a corpse is an object. (Both sides of this divide are addressed in answers to this question.) In short, ths DM reads the 5th-level Clr spell raise dead [conj] (PH 268)—that has as its target entry Target: Dead creature touched—as simply being a more specific target than case the 8th-level Sor/Wiz spell temporal stasis [trans] (PH 293) with its target entry Target: Creature touched. Unlike the spell raise dead that can only target (formerly) living creatures possessing the condition dead, this DM allows the spell temporal stasis to target living creatures, (formerly) living creatures with the condition dead, and nonliving creatures like shield guardians and liches.

Rulings may vary by table or campaign, of course, but even if the DM has dead creatures becoming objects rather than dead creatures remaining creatures, long-term corpse preservation alternatives exist beyond the now-nixed temporal stasis (see below).

Does a corpse in some kind of stasis retain its soul?

Probably. The 3rd-level Sor/Wiz spell gentle repose [necro] (PH 235) says that because the spell "preserve[s] the remains of a dead creature so that they do not decay" that the spell "effectively extends the time limit on raising that creature from the dead [and that d]ays spent under the influence of this spell don’t count against the time limit." This strongly implies that any method (or, perhaps, any magical method) of corpse preservation causes the dead creature to remain more easily returned from the dead (and if the DM rules that this is possible such effects would include having cast the spell temporal stasis upon a dead creature).

An unusual wrinkle is added by Complete Divine, the game's campaign-neutral source for a lot of information about death. On the Moment of Death says, "When characters die, their souls… linger in the body for a round or two[, and i]f the corpse was completely destroyed, they linger at the location of death. The last breath spell [originally CD 167-8 but updated on Spell Compendium 130] works the way it does [i.e. if cast within 1 round of the subject's death, the subject suffers no level loss] because the soul of the deceased hasn’t gone anywhere yet" (125). But Complete Divine implicitly contradicts the 8th-level Sor/Wiz spell soul bind [necro] (PH 281)—a core rules spell therefore from a primary source and taking precedence—, that says, "You draw the soul from a newly dead body[, and t]he subject must have been dead no more than 1 round per caster level." Hence the core rules say that souls loiter in the corpses for any amount of time… assuming an arbitrarily high caster level!

In other words, the core rules make the body–soul connection a little tighter, essentially locking the soul into the body either so long as the corpse is magically preserved or until a high enough level wizard can be found to bind that soul. But if using Complete Divine, the soul's gone to its final reward one or two rounds after the creature's death.

Thus magic is contradictory. This DM assumes that any effect that suspends a a dead creature's decay (or similarly, places a dead creature in stasis) functions like, by extension, the spell gentle repose; and that the spell soul bind does, in fact, work as written, and can yank a soul from a dead creature—somehow!—despite the dead creature having been dead any length of time… assuming an arbitrary high caster level (keep in mind, though, that binding the soul of a creature that's been dead for 3,000 years does require a caster level of 15,768,000,000—better get hackin'!); but that, otherwise, Complete Divine's ticking clock on the presence of a dead creature's soul only counts down from a maximum of two.

Besides maybe temporal stasis, what other means can preserve a dead creature for 3,000 years?

Below are several in order of convenience.

• Preserving the dead creature using unguent of timelessness (DMG 268) (150 gp; 0 lbs.) causes it to age but 1 day for each year that passes. Thus a wizard slain 3,000 years ago that's been preserved by the unguent of timelessness has a corpse that's as fresh and healthy looking as it would be after only 3,000 days—or about 8 years 2 months. This is well within the 10-years-per-caster-level limit of any typical cleric capable of casting the 7th-level Clr spell resurrection [conj] (PH 272-3).

• This answer's suggestion of accumulating enough material to submerge the dead creature by using the 4th-level shaper power quintessence [metacreativity] (XPH 128) is a fine one, although getting sufficient 1" dollops to submerge a corpse might be problematic without enough shapers on hand! (A quick Web search says that the typical human male's surface area is 1.9 m², but whether a quintessence dollop is like a drop of water, a pat of butter, or a sphere like a marble isn't clear from the text.)

• Sealing the dead creature within a husk globe (Libris Mortis 78-9) (8,500 gp; 700 lbs.) causes the dead creature "to remain perfectly preserved and on display indefinitely." Further, 1/week another creature can wave its hand over the globe and ask the englobed creature questions. Note: Yes, seven hundred pounds.

• Arrange a vigil for the dead creature, during which the spell gentle repose is periodically used on it. Or even say that what was used was a wand of gentle repose modified by the metamagic feat Extend Spell (3rd-level spell modified to a 4th-level slot at caster level 5,475,500) (32,850,000 gp/charge; 0 lbs.), although that probably sets a bad precedent, but such an item may have been the product of ancient magic now lost. (Even a planar metropolis (Epic Level Handbook 113-4) won't have such a wand available!) Alternatively, having much the same effect (but with far wider campaign implications) is a gentle repose boon trap (Dungeonscape 136-7) (15,250 gp; architecture).

  A more amusing version of the spell gentle repose is the 6th-level Clr spell preserve corpse [necro] (Book of Exalted Deeds 106-7) that delays a dead creature's decay and stores the dead creature in a holy symbol. However, whenever the spell expires, the dead creature reappears, and the spell must be cast again. This allows folks to prepare for the miraculous reappearance of the dead creature whenever is appropriate only to have the clerics use their arbitrarily-high-caster-level, relic-worthy staff of preserve corpse to return once again the dead creature to the holy symbol.