Hi kaygaffy,
When you are creating a pay run, you are able to set the dates for the Pay Run Ending and the Paid Date for the pay run - this also automatically determines the start date of the pay run based on the length of the Pay Schedule. There are no limitations when setting the pay period, so you are able to create a pay run overlapping with a previously created pay run at any time, and you aren't required to have deleted the prior pay run in order to do so. That said, if you do delete the previously recorded pay run, you would still be able to create a new pay run with those same dates when setting the pay period - you can check this article for more information on creating a pay run, or reply in this thread if you have any other questions!
-Lucas