L.N.
Unfortunately, no. They have no legal grounds to be able to keep the house. Also, many times in an 'estate' situation, the sale of real estate is not up to the survivors, it may be mandated in the will or a court may order it. It might not even be within their power to stop it if they wanted to.
I have to say, though, that 'cousin and husband' really shouldn't have to be accountable to anybody for the success they have had in their financial planning, or for their lack of children. Sure, it would be great of them to be able to help out this family, but the aren't obligated to do so just because they have been successful. The other couple's poor credit and job situation is not 'cousins' fault!
It sounds like the couple needs to sit down with a financial expert and make some long term goals as well as a plan to reach them. An attorney at this point will do no good since they have no rights to the house.
Sorry to sound so rude, I really don't mean to...I just get tired of hearing people blame others for their own financial irresponsibility. I really do wish them good luck!
~L.