Sister ghosting me as she owes me money

Another option is to sue her to recover that money- if you want to go that route

The most realistic one?
Consider any loans lost and say no next time.

I am well known for being persistent, but sometimes it really does pay off.
Write it off in your head, so it doesn't bother you unduly, BUT I would keep emailing / ringing every month (alternate) just saying you want to talk. If you can talk, given that you need the money for carehome fees for someone that presumably she knows & has been part of her family for ages, she may send you some, and that might be enough for bygones to be bygones and you still have a sister.
It's a big amount to put down to experience and, as someone who's never had a sister, hang on to them if you can.

Thank you everyone
I definitely will not lend any money to ANYONE anymore
I hope that my sister will realise the error of her ways and pay me back
However, I know deep down that even in this hopeful scenario, the relationship will never be the same again

Too late for you unfortunately, but as a principle never lend money (or anything) that you aren’t prepared to lose.

Highly unlikely you will get the money back as advised in previous post. Hope you really didn’t loan your sister a further £10000 “last week”!?

Your sister has chosen to ignore your calls and texts. Accept the financial loss and your sister cutting contact and focus on your life and loved ones in this country.

She won't pay you back....accept that and move in

I concur. This money is not going to be repaid.

Sadly, as well as losing the money, you will have lost a sister as well.

What NotSpaghetti says.
Don’t lend money again.

Sadly I think this is lost to you.
If you get anything back I'd treat it as a bonus.