Oooooh, that would piss me off. I would never do business with a bank EVER again if they did something like that to me.
Many moons ago, I was doing business with a very small, local bank and dropped my guard enough that they seized an opportunity to attempt to screw me with that scam. I had a mortgage with them, $26K in one account and ran another household checking account with a real tight balance. A miscommunication resulted in both my wife and I believing that the other had deposited our weekly paychecks. With an undernourished balance, the monthly bill checks started bouncing. The bank then decided to snail mail me a notice for each time they returned a check and removed $25 from our account. Once I received the first notice I headed down to the VP's office for a little "coming to Jesus" meeting. I asked if the $175 they stole on the first day had enough margin included for a 15 second phone call for a heads up? "Sorry but our policy is to send a notice". I asked if he was aware that the dollar amounts were carefully arranged to bounce the maximum number of checks, and that I could of rearranged the same checks, on the same day, and left $100 in my pocket? He declined to answer. I asked if he felt any sincerely when he proclaims himself to be a contributing member of the community, at this local institution, when he clearly is engaged in screwing community members? Once again, crickets........
Then we covered how this deal was going to wrap. First, we are going to deposit the two missing paychecks. Next we are going to undo whatever damage was done to my finances, including any upcoming charges by those who received the NSF checks. Third we are going to remove our collective banking head from our ass, and give some thought to joining the first world and offer overdraft protection, and automatic account transferring that can prevent this from happening again. Finally, if this doesn't work for you, the $26K in my other account, and the mortgage will be at a competitor shortly.
Somehow, they seemed to find a way to work it out. Since then I have left this backwater circus, and never had a problem again.