My understanding is that the individual memory cells just blink out like light bulbs when their state has been switched on and off a certain number of times. But the rest of the cells keep on working and so would the drive.
It's too early to tell, as A Guy pointed out, so very few people know what actually happens, but my guess is that you would start to get data errors and the capacity of the drive would start to diminish.
On a spinning drive a modern OS can identify bad blocks and flag them as unusable. I can't imagine why that wouldn't happen with an SSD too. Bad cells would be flagged as unusable and the drive's life would be extended, but like bad blocks showing up on a spinner, it'll be your cue to start shopping.