For the bank situation to work, they would have to add an unrequested service to your account and then attempt to charge you for it. i.e. Bank adds overdraft protection to you checking account and then bills you for it.
Say you have an internet plan with a 5GB download limit and after 5GB the connection would no longer send data, one month it lets you download 7GB and then they send you a bill for going over. You probably would not have to pay the bill since they changed their behavior and provided extra without prior notification.
To put a hypothetical example, if I fix a life threatening electrical or structural issue in a children's hospital unsolicited, whatever hit to my reputation I take by charging for unsolicited work, is dwarved and possible restored and reversed by the gravity of the issue fixed and the consquences avoided.
Of course this is contingent on whether the value was actually provided and whether it is provable.
Even if it would be legally possible (I don't think you can force your 'services' on an unwilling entity and then force them to pay), it would be absolutely awful optics.