Almost never — but yes, in extremely rare cases.
The most likely situation would be during a satellite tournament, when you're close to the bubble and don't need more chips to secure a seat. For example, if 10 players win a ticket and 11 remain, and a short stack is already all-in, folding AA could be correct if calling risks elimination and you're already safe chip-wise. In satellites, survival matters more than chip accumulation.
Another edge case could be under intense ICM pressure near a final table bubble, where massive pay jumps are involved, and you're in a position to ladder up just by staying out of the way of bigger stacks clashing.
That said, 99.9% of the time, AA is a snap call or shove. Folding it preflop is something you might do once in a lifetime, and only in very specific ICM spots. 😊