The house we inherited had a mortgage on it, albeit a small one (22k), with no protection/insurance policy to cover it in the event of the borrower's death (my father) as the policy had been cancelled literally a week after the mortgage was paid into my father's account. Prior to this the house was unencumbered.
Luckily (if you like) there was a car with a reasonable value and some premium bonds; we sold the lot and paid off the mortgage (just about). We were advised that if that wasn't the case then either my brother and I would have to cover the mortgage in full i.e. one lump sum (so basically taking out a lot of credit between us, we don't have much in savings being only 25 and 23 respectively) or handing the whole house (£275k) to the lender for them to see for **** all and then pass the difference on to us.
Looking at how much lenders sell houses on for (reclaim what's our's, anything else above that is not our problem) I wouldn't be surprised if they let the house go for £100k less than it's worth.
Inheriting debt is more than possible and the lenders are all too happy to 'take the problem away' from you.