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Polymorph Any Object gives an ability score to a stat when the target does not have an ability score:

If the target of the spell does not have physical ability scores (Strength, Dexterity, or Constitution), this spell grants a base score of 10 to each missing ability score

Undead don't have a Constitution score. In the case where an Undead is polymorphed into another Undead with this spell, what happens?

As far as I know, Undead don't use their Constitution, as they don't have one, but this spell seems like it would give them one back, but it would be a useless, empty stat, as their Charisma modifier would still be replacing it.

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I'm not entirely sure that RAW allow you to use Polymorph Any Object to turn something into an Undead creature (it "functions like greater polymorph", which is limited to living creatures).

But, that's a boring answer (and one I'd be unlikely to enforce as a GM), so let's assume that Undead can be created via Polymorph Any Object. I'm pretty sure that the creature would still have a Con of -.

First, Pathfinder's Polymorph base rules says nothing about Polymorph spells actually changing the type of the subject. Thus, the creature would still be an Undead, and would thus still have a Con of -.

However, that means that, technically, you could polymorph a wooden box into a human and it's type would still be "object". This is silly, so let's assume that PAO changes type and not just physical appearance. In this case, the result is an Undead creature. Undead still have a Con of -, so the resulting creature would, too.

One could imagine that, during the second or two during which the magic is doing its work, the target's body starts working again, so it might have a Con of 10 for a brief moment, but that leads to all kinds of weird edge cases with readied actions and such, so I probably wouldn't (at least, not in a mechanical sense; I'd probably be cool with it as a purely cinematic effect as a GM).

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I would say it does not. The spell gives the target all the ability scores it's missing. If that includes those that the new form does not have/need, then that would imply that if you convert a rock to a wooden log it also gains a set of mental scores.

That seems an entirely weird way to handle the spell. The logical reading would be to say that the spell fills in missing ability scores if the new form has a need for them, which means that an undead wouldn't get a Con score, and a brick wouldn't get an Int score. (Or any score, really)

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