Keeps losing remote in the bedu

If you stick anything on it, be careful not to stick it over the battery cover.

How about some of the sticky back Velcro?
Some on the remote, and some nearby.

It depends on the lady's disabilities but could you or someone sew a small material case with a velcro strap that would fit over her wrist.
I initially thought of attaching it to a lanyard but then realised that's not such a good idea although they do have a safety release.

fluttERBY123, does your friend have bedrails on her bed?

If so, you can look on Amazon, and they have several caddy type bags that hook onto a rail.