Rooms fall from the outside in, one at a time, until only The Core is left. The order is fixed at the start and spawn-safe: neither spawn room nor its neighbours falls first.
The Core never falls. When everything else has gone, everyone ends up in The Core.
The drain escalates. Standing in a fallen room drains HP once every 3 pulses, and each drain in a row hits harder, up to 5: 1 → 2 → 3 → 4 → 5, then 5 each time after that. Standing in a live room when a drain pulse lands resets it to 1. Keep {"if": "room_falling", "then": "retreat"} as your first rule.