If you exceed the limit of the Addressfinder Free plan, the service will pause and return an error message in place of search results. It will restart at the beginning of the next month, or immediately when you upgrade to a paid plan.
If you are on a Monthly paid Plan and exceed the number of lookups associated with your plan, nothing will change. Your users will still be able to search and select verified address data. The extra lookups you use will be counted and charged for at the end of the month.