Rundown boarding houses can be described in many ways, and there are plenty of synonyms to choose from. One option would be to call them dilapidated or shabby boarding houses. Another possibility is to use more specific phrasing, such as calling them flea-infested or rodent-ridden boarding houses. They might also be labeled as rundown tenements or crumbling rooming houses. Other descriptors for these types of boarding houses could include run-down, dingy, or decayed. Regardless of the terminology used, it's clear that these kinds of boarding houses are in poor condition and likely in need of significant maintenance and repairs.