The problem I have with it is for example the following rare case:
Assume a player has 99/100 pixpets in his inventory.
Along with that he has placed a bid of 1000 PC on an, let's say Albino Xeldron Egg, which will be the highest bid in the end.
In his lunch break and 2 hours before the auction ends one of his PPs returns from a hoard with an egg. He puts it into his PP inventory and returns back to work not realizing, that his PP inventory is now full.
Returning home from work 3 hours later and back on his PC he reads, that he has own the auction. Happily looking through his PP inventory he finds ... no Albino Xeldron Egg. As a result he complains to you, that due to a bug he didn't receive the egg.

And now its up to you telling him, that you won't return the egg and that its all his fault, that he didn't free up space in his PP inventory before the auction ended. Have fun!

Conclusion:
Its kinda obvious that such a scenario should and can be avoided as much as possible but never 100%. And there are race conditions, where a player clicks add to inventory the same time an auction ends.
My suggestion would be to allow an overfilled pixpet and/or item inventory for those rare cases but block any other player action involving the corresponding inventory (e. g. no more send to hoard and can't move any PP) until he removes/discards a couple items/eggs.

[Edit:]PS: I don't intend to point a finger at you. I just want to avoid the frustration that might be result of such a rare case. So don't feel offended though I'm being a bit sarcastic and nitpicky about a potentially rare case here.