My mother's late partner was like him - refused any conversation around making a will, and died intestate.
Luckily and much to the shock of his vulture family the house is entirely hers. Not his. So she's safe.
You aren't. You're thinking like a 1950s housewife but with none of the rights and securities they had as married women.
At the moment you're in a cul de sac - your anxiety transmits it to him whenever you try to speak about it and he gets defensive and shuts down.
You're pinning all your hopes and expectations of security in vulnerable old age on a man who won't talk about it, won't listen to you and hasn't made any provisions for your future.
But then - have you?
Have you made a will yourself?
Regardless of what you own, do it / update it, involve him in that process so that he sees it's nothing to be afraid of. He may have developed a superstition around it (I think mum's partner was inclined to that).
Start thinking and behaving in terms of what you are - are single independent woman who happens to pay bills to live in a man's home. You're basically a rent-free lodger.
I don't see here if you have a job/income/pension or how old you are, how close to retirement.
Get up, stand up, take control.
If you are in work, and hopefully you have a separate bank account, put a percentage of your income into savings. Also separate.
Get a pension review. Where do you stand? Maybe start a private pension.
And look at flats. Estate agent windows will give you an idea of prices. Owning a property however small is a great investment even if you don't live in it, and rent can be a source of independent income.
Talk about your plans and decisions with him. Present yourself as an independent single woman standing on her own feet, earning, planning for her future - and not utterly dependent on him.
He may realise you could possibly exist outside of him and his cosy co-bills paid arrangement might end, leaving him in some of the vulnerable situation that's your normal.
This could have several results; be prepared for them all.