As I understand it, it doesn't matter if they are Chase, or BECU - most banks don't actually own any of the mortgages they issue.
The problem in 2008 was the fraud, the irrational exuberance, and really dumb investments by the investment branches of a few investment banks. The retail arm of, say, Wells Fargo, which issued a whole bunch of shitty mortgages was fine.
Whether or not you think that investment branches of banks deserve to be bailed out is an exercise for the reader.
Not being funny, but Guiliani forced the whole mortgage banking business into insolvency to make a point that some still think was Vendetta. Whatever the case, Guiliani forced a vast capital market to halt, for no reason I've ever learned, and handed a four trillion dollar bill to the taxpayer, for kicks. No wonder Trump likes his advice.