I'm thoroughly confused by your post.
1. Mary is now in residential care.
2. John (Mary's brother) is her care representative.
3. Mary's home is empty.
John ( is it John or some one else?) is proposing that you live in Mary's home effectively rent free; presumably so as not to leave it empty/unheated/uninsurable for a number of years.
As far as John's legal authority goes, I don't believe he has the right to dispose or rent out property on Mary's behalf; but presumably he has been taking care of business on his sister's behalf.
Whatever agreement is reached however ends once Mary passes away, even if there was an EPA it ends on Mary's death.
The only question you really need to concern yourself with is if the arrangement suits you, being aware that you will have to vacate on Mary's death.
Personally if I were John, I'd be very cagey.
IANAL