Legal Question in Real Estate Law in Oregon

That is actually a complicated question. Ordinarily, if he dies without a will, you inherit the house and the debt. If he has a will, it can specify that his estate pays off the debt before the house is transferred to you, but it does not have to (and his estate may not have the cash to pay it off). It may also be possible for you to "disclaim" the inheritance, if the mortgage is bigger than the value of the house. You could also allow the house to be foreclosed.

In general, I would say that you will be legally responsible for the house in much the same ways he is now legally responsible. If you do not want that responsibility, have him execute a will that gives the house to someone else. That person can also disclaim it, however, and as wife you will be the "residual beneficiary" and get the house (and the debt) anyway.