Absolutely not, in this situation.
I think in general, co-signing should be something done rarely. My parents generously co-signed with us on a house, under the following conditions: they could afford to make the payments if we defaulted, we had a *huge* downpayment from savings, they knew that barring death and destruction we wouldn't
default, and although I was a sahm and we had a very low income they had seen dh and I live frugally and knew that he'd work his rear off in order to pay the mortgage.
In other words, they cosigned not to "save" us from our stupid financial mistakes, but to give us a boost in the direction we were already going. We couldn't get the loan on our own because my age, and his newness to the country meant that neither of us had any credit history.
However, if I could go back for a do-over, I'd rather rent for a few years and do the house thing on our own. There were no financial problems, but there was relational tension because of the loan. Even though dh agreed to it, it still felt to him "intrusive", and I think my parents were totally well meaning but felt that the financial partnership gave them an opening into our personal lives that was uncomfortable for all of us.
If you co-sign to rescue someone who is currently in deep financial doo-doo because of poor choices, or who has a history of poor financial choices, that's pretty much saying "Problems, start knocking at my door!!"