I can think of a few options:
A: Poss ignores Delay anyway
B: No one dies and chronomancer isn’t told of an attack.
(Your options reworded for clarity)
C: The target is attacked with an unhealable attack which get’s delayed. The possession aspect is removed but the target still dies (eventually)
D: The possessor swaps bodies once the delay timer runs out so long as they are still alive.