Does he know she's saying these things?

Look, we're all amateurs here, but I would suspect that she's picking up on him saying similar things. You're obviously doing all you can to instill a strong sense of self-esteem in her, the only other thing I can think of is some activity that makes her feel she is useful to others whether that's gong to feed the ducks (the ducks need us to feed them to survive) or visits to an aged care home (you can't die, Mrs X needs us to go and have a chat with her) etc. etc.

DD1 had a phase where she talked about death a lot - didn't want me to die etc. etc. I know it's different, but I emphasised how neither she nor I were going to die any time soon because we were far too busy and talked about our future plans. That seemed to calm her down quite a lot and the phase has passed.

Huge hugs. I don't know where her dad has some sort of disorder or is just a lazy turd. Either way, not on to have a child on a custody visit and not have food in the house.