I would do something like this
1) Register the date and time the user registred/started the "pending period" in a database
2) Create a cron job / scheduled task (depending on your OS) to run a (php) script at a set interval. This (php) script fetches all the pending users from the database where the "pending period" is equal to or greater than your specified time limit, and then do whatever you want to do with these users.