COB Bids Confusion

So I understand that the official “bid day” is on Sept. 11th and sororities can still extend a bid after that date if they haven’t met quota for whatever reason. Let’s say hypothetically a PNM has gotten invited back to all the recruitment rounds of 2 sororities but on bid day she only receives a bid from sorority #2 when the other was her favorite, and she accepts #2’s bid since she still liked them. But let’s say sorority #1 ended up with some bids left to give since maybe the girls they chose accepted bids from other chapters, and they try to extend one to this PNM another day but she’s already accepted another bid since she thought she wasn’t getting a bid from #1.

Will the PNM not be able to change her mind? Is there gonna be a cut off date where bids won’t be extended anymore so PNMs can make their choices without hoping to expect a bid somewhere else to prevent this (ik the point of COB is in the name but this seems like a gray area, LOL)?