Having read gracesgran's ordeal with the company wanting to call on her mum I thought I would share what we did with my mum.
When mum was home alone any random caller was met with the door chain on and my mum would say hang on I'll get my son he deals with that sort of thing. Generally my brother was at work but more often than not just her saying it was enough to send them on their way. She did the same with random telephone callers.
She always kept the door chain on and even when we visited it was there but I was happy about that. I said just because you expect us at 2pm don't take it off because you don't know if someone will call before we get there, luckily she did that. Better to be safe than sorry.
When my MIL goes out she has a handbag that has a long strap that goes over her head and body and keeps the flap closest to her body at the front. That way no one can grab at her bag as they pass or dip into her bag. MIL has macular degeneration so obviously her sight is not good, therefore anything to keep her safe is good.
Not in my family, but I knew of a lady who kept a policeman's helmet and truncheon in the hallway on view to any random caller. It worked, people not genuine made their excuses to go I believe they were fancy dress items she picked up but were genuine enough if no one got too close. Of course you don't have to go that far.
But it isn't just our elderly relatives who are targets for opportunist thieves or callers so we must protect ourselves too.