Wait. He died and you didn't go through probate court to establish ownership of the house? Did he die recently??? Without life insurance? What about PMI mortgage insurance? It might pay on his death, too.
I'm sorry for your loss. It takes time to get through probate, if you had no living trust.
And for your pending loss! Selling short is not a good plan if you can avoid it.
You will have to clear up the title before the sale is complete, by going through probate (or exercising your living trust). Authorities have to establish that your husband died (not by foul play), and that the name on the deed and mortgage is indeed the same person.
So, I'm going with "TRUE". Before you can sell, you must resolve matters with the estate. His debts must be resolved as well, but only if they were secured by the house.