I would do ANYTHING for my (many) nieces and nephews. Donate a kidney, give them a place to live, stash their stuff in my garage for umpteen months while they figure out a permanent living situation, lend them my car if they needed transportation for a few months to school or a job. I would kick in X thousand dollars (if I could at the time I was asked) if that would make a loan unnecessary, I would happily give what I could afford as a gift, no strings attached, with the assumption that it was going to tuition or to pay down an already existing loan. I would do whatever I could to help get a job, get into grad school.
I would not cosign a loan on their behalf. I see a world of trouble with this plan, starting with your husband’s relationship with the person who asked.
What happens next year when this relative takes off for Aruba or Disneyworld over Christmas while you guys stay home and enjoy a modest celebration? What happens when they upgrade to a big screen TV or trade in a 4 year old car while you are still driving your clunker? And the biggest risk- of course- what happens when the college kid in question decides “I don’t need a BA- I’m going into business with my boyfriend and we’re going to make a million dollars off our App idea”. Kid drops out- loans come due. Or kid has to take a medical leave-- it happens. Or one of the parents becomes disabled- it happens.
Kick in what you can for college kid’s tuition, cross your fingers and hope this kid can finish. This is the early stages of a spiral which can’t end well if you are on the hook or in the middle of it. Do you really want to be asking a relative “why the hell didn’t your kid find an affordable college”, or “why the hell can’t your kid live at home and commute to save 15K per year” or “Why are you in debt over a kid who has a C- average and is majoring in beer pong?”
You do not want to be asking these questions because you do not want to know the answers. Turn this one away and be thankful you’ve dodged a bullet.