Murse,
Some of the responses have been a bit harsh. IMO.
It sounds like your parents had a temporary (up to 5 year temporary) no income situation, they ignored so many important things, but now could move forward with $80k/yr income and only $1k/mo mortgage payment. As other notes, between mom, brother, uncle and aunt, there are at least FOUR adults capable of helping to pay the mortgage now.. even with part time jobs this is possible.
Therefore, if you can help them with good budgeting sense, I don't see why you would not be repaid for the $50k eventually.
Agree strongly with the following points:
a) Talk to a real estate lawyer about it and the foreclosure
b) don't co sign.
My initial thought was for you to buy the home, take the title to it (or another smaller place), but if your parent's situation truly is "temporary" and now resolved, it may be worth the risk and reduced hassle to gift or loan the $50k in return for a second position on the property to secure it. (See lawyer).
-----------------
A key issue that has not been addressed well yet -- your uncle only paying a low rent of $600/mo, and then only paying it from time to time.
Your parents do not have the $'s to pay someone to fix up old vehicles for them, they need the rent in cash. (because they are about to lose their home over it!)
Also, your uncle should be paying closer to $800 per month (assuming the whole home would rent for $1600, his share for his family would be half, 6 bodies use up a lot of home, the only exception is if they just rent a tiny basement suite separate from the main kitchen and living areas),
PLUS he should be paying his family's share of the increase in utility costs. A whole family and little kids use a LOT of utilities, by the way.
It is very likely that right now your parents are actually spending each month to support your uncle's family to stay with them -- paying extra CASH on utilities, maybe food? while waiving any rent because of the car fix ups.
Good luck. As long as you don't co-sign anything, it sounds like your personal risk is limited to 8 months worth of savings.