One of my close relative just passed away and I have taken on her cat. I know that her cat was not insured and that she had quite a large outstanding bill at the vets and although i'm not sure of the exact sum I suspect it's well into 3 figures. I know for sure that I can't afford to pay it off and the cat also looks like it will need quite extensive dental work in the near future which is obviously going to be expensive. Is that debt now mine now that my relative is dead? I've never had to deal with anything like this before so I don't know what to do. I'm sure there will be enough money in the estate to pay it off eventually but it is going to be months before the will is sorted out.

I have to take one of my other pets to the vets on Tuesday and was wondering if I should mention something then or just leave it?

Debts are against the deceased's estate, they are not inherited. Its the same as any other bill like the electric, window cleaner or milkman. The executor of the will should have access to the deceased's bank account to pay for these bills. If there isn't enough available cash then I'd imagine all people owed money will have to wait until after probate when all assets will be disposed of.
So you need to liase with whoever is acting as executor about this - though it's likely they already know.
As for future treatment I'm not sure if an insurance company will pay for problems that are 'known'. You'll probably have to pay now and hope your inheritance covers it - I guess a trip to the vets should get an estimate.
Sorry for your loss, but I'm glad you've taken on the little one.

They still have to be paid I think.

Yes, but not by indie_star. Shrike's post explains it all.

Thanks for the help. I don't think i'll mention it at the vets tomorrow. They'll have to know when I go back to sort the cat's teeth out so I guess i'll find out then what the exact figure owed is then i'll plan what to do next accordingly.

The debt would die with them. Unless the vet decided to pursue the case for retrieval of the money owing in court, and the deceased person's estate could pay it.

Indie star you can't be held accountable if it can't be paid from the estate. But keep us posted!