These (at least a few years ago) are also in some landlord-agency contracts. One I've seen stated they were entitled to 10% of the rent if the tenant stayed aft

These (at least a few years ago) are also in some landlord-agency contracts. One I've seen stated they were entitled to 10% of the rent if the tenant stayed after the end of the original tenancy without a gap in the tenancy, even if you are no longer using their management services. I never pursued it to see if it was actually legal - a strongly worded letter indicating that there _was_ a gap in the tenancy (a day, but it satisfied the strict wording of the contract), that the tenant was considering leaving due to the agency not fulfilling its contractual obligations, and that other properties would be removed at the end of their tenancy if this was the case, settled the issue without having to go that far.