When one co-borrower dies who is responsible for repayment of an equity note, the other borrower or the deceased's estate?

The parties to a contract are the ones that are liable in the event of a breach.  in this case your dad and his wife were both obligated to pay a equity note regarding the property your dad soley owned.  When your dad passed away the property went to his wife.  if the wife fails to pay the note, the bank may forclose on the home.  if you want to keep the home and the equity note in place, i suggest that you make sure that the note is paid and that there are no delinquencies.  If the wife does not care about the house and rather move somewhere else, then she may neglect the payments.  you need to find out what she is doing and whether she is able to pay.