How do you deal with worrying that your dementia relative will walk out the door while you are sleeping?

Put a double-bolt lock on all doors. Keep the keys on your nightstand. If you have a patio door, get a lock/key pole to slip in the bottom rail.

There are many alarm devices for people with dementia from mats at the side of or in the bed that sense when someone is getting up to motion sensors for hallways and door alarms. Depending on the person's mobility one of these should do the job.

Inside door/window locks they can't reach and door alarms. Worry is just part of caregiving and does no good at all.