Hi OP,
Another one speaking from experience, my 84 year old mum who lives 50 miles away from me.
She had a lock where you could put the key in on the inside of the door which she did. We speak most days so when she didn't answer her phone after ringing a few times that made me worry.
Short version is she had collapsed and couldn't get up. Although she has a key safe because the door key was in the lock no one could get in, it ended up being an ambulance and fire brigade job.
The fire brigade changed the lock to a thumb turn one on the inside there and then.
She also now got a pendant to wear, it costs about £30 a month. There's been a couple of times when I've not been able to get in touch since it happened reasons like phone not working and her unexpectedly going out 🙄
If the neighbours weren't available to check then I've phoned the pendant people and asked them to contact her through the pendant which they have done.
My mum wasn't always wearing her pendant, she wasn't putting it on between getting up and getting washed and dressed after breakfast and between putting her PJ's on in the evening and going to bed but after I explained that anything can happen at anytime and the panic I feel when I can't get in touch she now wears it from getting up to going to bed.
I know a previous poster said not to put a chain on but if that was a compromise that needed to be made for your mum to feel secure then I'd do it on the basis that if someone can open the door then it's not that hard to force the chain but it's pretty difficult to force a door.
Luckily there's been no medical episodes since, my mum was in hospital for a few days but that was due to the effects of being on the floor and what it does to your body being in one place for a prolonged period of time.
I'd prefer her to live closer to me but she's not ready to do that yet but her having the new lock, key safe and pendant is a compromise that works for both of us currently.