Debt?

My mother in law brought it up to me today that she needs to go to town hall and let them know my husbands father passed away over 3 years ago because his name is on the trash, water and sewer bill for her house. She said she doesn’t pay it and she’s been letting the debt just collect. She said she needs to tell them before it ends up being my husband’s problem since he’s next of kin. Can this debt really end up on my husband? He doesn’t live in her house or anything. I understand he’s next of kin, but it’s her house and she’s not paying her bills. But then again, they were divorced before he passed away. So I guess it’s not her problem if it’s in his name. But I’m also confused how she can just get away with using a deceased person’s name to pay (well, not pay) her bills? Is that fraud in any way? I’m genuinely curious, I completely understand why it could end up my husbands responsibility but just curious if anyone might know the answer to this