Can an association sue the renter?

In America, most anyone can sue most anyone else for most any reason. If you can find an attorney to take on your case, that is.

In particular, an association may pursue an renter when the renter's occupancy in an association's community cannot be controlled by either the owner or the association, and the occupancy violates the governing documents in some substantial way.

In advance of bringing any suit, however, the association is best advised to review the steps involved that are required to 'control' the occupancy of any resident.

If you are a renter, you are subject to the provisions of the governing documents, and you can be in violation of them. When you are in violation, expect repercussions to follow.