The bank that currently holds my mortgage was one of the ones that failed circa 2009.  It got taken over by the government, then sold to a bigger bank, then later sold to another bank.  Thankfully this had absolutely zero effect on me as a mortgage holder, aside from worrying that it might have an effect on me as a mortgage holder. 

I just got a letter in the mail from this bank offering me a good deal on refinancing.  I'm actually thinking about refinancing anyway, but I'm hesitant to go with this bank because it feels like I'd be rewarding failure, and that's not something I really want to do. 

Related:  Advertising a failure