Caregiver liability - noncompliant patient

Hello.  My mother cares for my father who had a stroke approx 3 years ago.  He can walk with a cane but there is always the risk that he willl fall.  If my mother tries to convince him it is unsafe to go on a walk outside due to weather conditions or otherwise, and my father ignores her instructions, is my mother liable for neglect of some kind?  Thanks for the help.