A human being is under the effect of the Curse of Circe, but with a moon duration. A few days before the spell expires, a second spell is cast on the transformed human, but this time a muto animal (also with moon duration) which changes the pig form into a completely different pig. My question is what happens when the original spell ends?
The Curse of Circe is muto corpus but the second spell is muto animal. The second spell was acting upon the animal body of the transformed human. When Curse of Circe expires does the second spell also end since there is no animal form upon which it works?
You should read HoH:MC p.22 box Ringing the Changes for details and pitfalls, if you delve deeper into stacking shapechanging effects and powers.
But in general, if a magical effect takes hold it runs for its own Duration. There is, also for the sanity of the SG, no continuous checking for still applying conditions - magical or otherwise - that were needed for the casting of that spell. See for this ArM5 p.112 Duration. An important example is, that a T: Boundary spell does not expire or move if boundary markers (like lake shores or city walls) are moved, tampered with or obliterated.
There is also some question (YSMV) as to whether the second spell would even take effect since the essential nature of the transformed man is corpus, where Animal is merely its apparent aspect.
We know for sure that spells do not fail this way canonically. Consider a Bjornaer. In human form Creo or Mentem spells have a valid target, while Animal spells have no valid target. Meanwhile, in animal form Animal spells have a valid target, while Creo or Mentem spells have not valid target. Do such previously-cast spells fail when the Bjornaer shifts to the form for which they have no valid target? Explicitly not. So we know requiring a spell to fail for a currently invalid target that used to be valid is non-canonical, just a house rule.
Now, some spells might not be effective without failing. Consider a MuAn spell on such a Bjornaer to make its tail prehensile. When the Bjornaer switches to human form, it has no tail (assuming standard human form), so an effect making its tail prehensile is ineffective even if the spell hasn't failed.
A Bjornaer transformed into their heartbeast is entirely a different matter than any other transformation, and it's not a useful example - those spells don't have an invalid target. If a Bjornaer changed into any other form - something they would rarely, if ever, would do - they would see the second spell fail.
Yes, they explicitly have invalid targets. You cannot use Corpus nor Mentem on an animal Bjornaer. You cannot use Animal on a human Bjornaer (leaving out wards here). The Bjornaer is an invalid target for them in those situations. So when the Bjornaer shifts, the target is now invalid, but the spell keeps going.
Of course part of this is that bjorner manage to change their essential nature- something no other hermetic ability can do, so the way in which spells transfer still isn't the best analogy.
Bjornaer are more resistant to spells of incorrect (relative to current shape) Forms that are other shapeshifters.
Hermetic magic, without being Bjornaer specific (could be any caster), is not invalidated with invalid targets so long as the original target was valid in this case.
Can we find anything that actually goes against these?