An elderly demented person who likes to wander poses a problem for families. Even the most watchful of caregivers can have a temporary loss of concentration and/or get distracted and lose a loved one who was under their watch.
Leases are often used for kids and considered acceptable, in some settings, by many:
Maybe we can come up with an adult-sized version? Just be prepared for a possible reaction when you try to attach the leash to your loved one with dementia: