Dr. Urza, PhD of Dungeon Crawl
Dist of Columbia
I would suggest revisiting the raid flow chart. When placing a counter it directs you to place it adjacent to an already placed counter (not necessarily the most recently placed counter) that is closest to the nearest family in terms of the sum of the area values. Alphabetic priority breaks ties.
If you do this I think it is impossible to hit a dead end. You would veer off before then. Though I am sure someone will come up with a weird corner-case...
Eventually, every family (save those that are inside a fort) will get moved to the Caught/Escape boxes, or the raid counters will be exhausted. In either case, the raid will end. (and in the former, the leftover raid counters are used for some action) Families can't coexist with a raid counter -- if one enters their area, they evade, escape, or are caught one way or another. Given enough raid counters, every (non-fort) family will end up in Caught/Escape.