If you are short an in-the-money option when expiration Friday rolls around, and you choose not to cover it, then you will be assigned. If you are short a put, you'll have long stock Monday morning. If you are short a call, you'll have short stock Monday morning. It's that simple. Even if the option is just barely in-the-money, you will be assigned. There are very rare incidents where assignment of slightly in-the-money options does not occur, but the odds are very much against it. If an ITM short option does not get assigned, then someone just left money permanently on the table. That doesn't happen very often... and certainly not on purpose. Assume you will be assigned on all ITM short options at expiration.

Letting a short option expire can often be the cheaper way to go in terms of transaction costs. For example, the difference between the bid price and the ask price of options is either $0.05 or $0.10. If you want to cover a short option at expiration, you'll pay the ask price, which will be atleast $0.05 above the bid price. For a single option contract, that's $0.05 x 100, which is $5.00. For ten contracts, it's $50. Plus commissions. Those nickels add up! You can keep your nickel if you just let the option expire. However, you must be cognizant of the new position you'll have upon assignment if the expiring short option is ITM.