If I'm long 1 call at expiration that is ITM, and I exercise, someone that is short 1 option will deliver 100 shares to my broker. If they are long, they delivery 100 shares of long stock. If they are not long, they delivery 100 shares of short stock and their brokers must go out and borrow the stock to make good delivery. After the assignment is executed, the process is no different than selling stock short.
Yes, I was looking at the volume today on HLT options and got confused about the stock borrowing on naked short options part for a while. Time to sleep I guess...