In this framework, you don't take the blame for others' mistakes. You take the blame for your team's mistakes, and take responsibility for fixing them. You explicitly do not place blame on the person who actually made the mistake, nor do you imply that you should not have hired or trusted them.
Obviously, all this assumes that it actually was a valid mistake. In the rare case where the failure was caused by gross negligence or intentional misconduct, then you should take responsibility for hiring and trusting them, and then you should fire them.
Obviously, all this assumes that it actually was a valid mistake. In the rare case where the failure was caused by gross negligence or intentional misconduct, then you should take responsibility for hiring and trusting them, and then you should fire them.