Legal Question in Wills and Trusts in California

They will request payments, and eventually foreclose if the estate does not pay.

If the deceased borrower does not pay than the lender can, and certainly will, foreclose. Depending on what your deal with the deceased borrower was (i.e. why were you on title, were you paying him rent, etc.) either the lender or the borrower's estate might seek to make some kind of claim against you. Keep in mind that, depending on the type of deed the house may now be yours.

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The property is subject to the deed of trust. The beneficiary (lender) can foreclose when the loan is defaulted on. I don't understand how you can state that you are on title, but then refer to someone else as the owner, and state that you do not want to purchase the home. You either co-own the home or not.