We have discussed pendant alarms before which may help-
The last post in this discussion mentions a fall alarm. I have no experience of these myself but after putting 'falls alarm' into Google, there seems to be plenty on the market. It may be worth having a look yourself or contacting your OT if you have one or social services to see if they can help.
I have "Lifeline" which is basically a "falls pendant alarm" where you press the button for help.You nominate the responders.