I know I am going to be in the minority here but I just had to add some thoughts.
First of all, personally in the same situation if I had the money available and had a good relationship with the family member I would definitely lend the money - at least the first time around. BUT... I would have to make sure that I was okay with the fact that I could very well not get the money back and would not let that damage our relationship in any way. As others have suggested I would not "gift" the money as to me that opens the door for future "gifts" and I would not want to start that habit.
But this is going to be one huge area where my opinions differ. I would definitely NOT put anything in writing. To me I would be doing a family member a favor, and if they valued the relationship as much as I did they would pay me back in time - however if they chose not to I would walk away knowing that I did a family member a good deed and that I knew I could very well not get the money back. I would most likely never lend them money again but I would not harbor bad feelings. But to put it in writing would be more like a business venture to me and it would make things awkward and tense. At that point no longer am I graciously trying to help a family member but I am enetering into a loan agreement. And that does not represent a family relationship to me. I know if my family member needed money badly enough to ask me for it then they do not need to be further humiliated by having to sign a contract, etc. If that is necessary then perhaps they should be visiting a bank and not me. To me it just strongly goes against the grain of family and what that represents. Sorry, just my opinion!
And some have degraded this family for not having any savings to depend on - but noone has bothered to ask many questions before passsing judgement. Times are tough folks, perhaps this family had savings and it has been used up already. None of us can ever honestly say we have enough left to survive comfortably no matter what circumstances should happen to come our way. I know many say that you should have a 3-5 months of mortgage and bill money readily saved - I am here to tell you that is not nearly enough!
Let me give you a flip side example to some of the stories you have already heard. Last year my DH was laid off in Oct. 07. This is pretty typical for us as he is a union construction worker and we are used to long winters off most years. For that reason I hoard money and save year round so that we are always comfortable during those times and live comfortably without relying on savings. However in Nov. a medical issue came up and he required surgery. He was medically out of work until March and just before being released another surgery became necessary. Normally March would find him working once again, but medically this was impossible. We were just about set to return to normal and his gallbladder decided to act up and the first week of July found him in the hospital again. Total last year he had four surgeries, all of them necessary immediately. And September he started a 6 month chemotherapy course which he is currently still undergoing. He is the solo bread winner in the family and I was willing to go to work and try to help make ends meet however we were back and forth to drs. hospitals and chemo and he was unable to drive - I needed to be home. I might also tell you I am only 36 years old and never expected my life to take a turn like this. By the time late October 08 rolled around things were getting pretty bad. A year prior we had already cut out most extras, and had changed our lifestyle drastically, no more eating out, bowling, movies, going out with family and friends. My SIL frequently asked us if we were okay and how things were going. When I replied we were okay she often commented on how amazed she was that I had enough put away to keep us going and that they would of lost their house in our position. That felt good to know that many others would of fallen long before I did but still as time went on - it was gettig harder and harder. One night while talking to her right after chemo started and the effects were taking place I burst into tears and just snapped. I told her I was not sure how much more I could handle and I was not just talking about finances - everything was getting to me. We were going to their house that weekend just to play some games and spend some time together and SIL came over to me and handed me a check. I was shocked and told her DH would never agree to this and that I could not take it. She assured me that if it made me more comfortable I could keep it between us and not tell DH. The next thing she did was took my hand and gave me a wad of bills and said and this is in case you guys need some cash right away. Please let us know when you need more. I cried that night for hours and eventually did tell DH what had happened. He called his brother and SIL and tried to return the money they refused. They said they needed to know that he could relax and recooperate and not worry about finances. DH reminded them that he was not sure what the future was going to hold and when he could resume work. They told him it did not matter. We emphatically told them as soon as we could we would begin paying them back. They were so graceful and understanding it was amazing. And DH returned to work about 1 1/2 months later. He works when he can and does not push himself further than possible since he is still in chemo. I have found lots of ways to earn extra and we did pay them back faster than we ever hoped for. But I have to tell you they were our angels - I don't think I ever would of asked but then knew us well enough to know what was happen, they saw the changes and they saw us struggle to hold things together for over a year and they reacted. We will never,. ever forget that! And our relationship has grown so much stronger for that. We were close before, unbelievably close but now we know exactly how much we would do for the other. And you know - I am not ashamed that the savings was not enough - I am not going to apologize for not being careful enough. It happens - circumstances far worse than you think are imaginable can and do come up. Family should be there during those rough times! But then again family can easily take advantage.
But I will say follow your heart and your instincts. Only you know what type of people they are. Only you know if they have really tried to make ends meet without asking your aid, only you know if theyhave any intention of ever paying you back. And only you know how this will effect your relationship either way. I believe instinct is an invaluable tool and all too often we cast it aside.
Anyways, I have rattled on long enough and I apologize to all of you for doing so. But it hurt to hear some of the judgements being tossed around. Believe I never, ever expected to be in the shoes I found myself in and it isnot a pleasant place to be. Please know we will keep you and your family members in ourt prayers and hope that this is the start of a new beginning for all of you.
. Now, they may not in their area but hear me out. I was playing around with a friend that moved to Georgia (they were a little strapped b/c they just purchased their first home) and I went on the web site for her power co. (I think to help answer a question for her) and I saw that you could purchase gift cards for electricity. Why not try to help them in this way? Maybe paying a few utility bills would ease the burden and then they could at least make a partial mortgage payment. 
Just not fair in my humble opinion..... Good luck OP, I'm sure you'll do what is right for your family.
to my Sperm Donor ( I cant even call him my Dad ) and I am still waiting after 11 years for the 5 months to be up that he said it would take to get it back to me 
