This isn't legal advice - speak with a competent estate attorney in your (and / or your Fathers) state, laws and experiences vary greatly from state to state (with the NE states being particularly archaic in their estate laws and probate processes versus the western states).......
Having worked a long time ago in title insurance, I got to see quite a few probates. I've also dealt with one as an executor. The debts of the deceased are borne by the estate, to be paid out of the estates assets - the don't pass on (unless you were fool enough to take them on by co-signing - never, EVER cosign a debt unless you're willing to pay it off 100% yourself).
If the assets of the deceased are insufficient to pay the debts, the estate will be declared insolvent (or what ever is the exact lawyer term) fairly early in the probate process. Those that are the beneficiaries of the will / estate (kids, grandkids, etc, either named in a Will or per law if there was no Will) would get zilch, nadda, nothing in that case - everything would be sold to pay the debts first. Oh, and if you're the executor, be sure you do your job by the book, especially if the estate is insolvent. In my state, an executor can be held personally liable if they fail to notify creditors or try and shaft them - the attorney was crystal clear on this point.