I wish I'd been more aggressive about this when my mother in law died. She left behind a house, but also a half a million dollars worth of medical debt from a decade of chronic illness that eventually took her life. We thought "fine, we'll let the creditors fight over the house and be done with it", but they refused. They told us it was our responsibility to sell the house at at least market rate--which was hard because it had several decades of deferred maintenance. They would only take cash and refused to do any work for it beyond making threatening phone calls about garnishing our wages if we didn't get it done in time.
Since it was the state Medicaid office harassing us I really didn't want to get in a legal fight so we did all of the work of selling the house. Our lawyer did at least manage to get our costs taken out of the closing fees so we weren't out of pocket except for the time and effort and miles since we live in a different state. All in all I can't recommend having a loved one die.
The worst part is back when my mother in law got sick my wife convinced her to write us out of her will because we were told that the state would get the home anyway after her medical bills piled up. What she didn't tell us is that she just changed her will to name her church as the beneficiary. Once we read the will it became yet another mess to clean up. It should have been easy enough, we talked with the pastor and convinced him to refuse the estate easily enough. Unfortunately the church board overrode him (I think they believed we were trying to pull a fast one), and then found themselves in a fight with the state over a house they also had no intention of putting the effort into selling and also a huge medical debt. It was very tempting to just drop the thing and walk away at that point, but it was clear the problem would never be resolved and it would almost certainly come back to haunt us in the end. We had to do the work because nobody else was going to. I never did get a clear answer from the Medicaid debt collectors why they couldn't just put the estate up on a government auction. I think it would have required them to do some work and they really just didn't want to.