I can think of numerous translators that don’t quite make it to their COL due to tropospheric propagation. KVGC’s FM translator is licensed to Jackson, CA with a 99w transmitter about 8 miles away on a mountain. It is virtually impossible to hear in the nearby towns year round due to line of site from KOIT in San Francisco. During the summer, it can be downright difficult to receive due to KOIT and KLCA in Tahoe. Generally, old town Jackson is fairly reliable reception year round...anywhere else in the area outside of that valley, good luck!
Besides stations not operating within licensed parameters (including STAs), I can only think of a few “full service” stations that do not really cover their COL. Now that TV repacking has begun, there are several stations that sold their spectrum that cannot realistically serve their new COL without cable coverage.
Best example of a FM I can think of is WGRQ (a station serving the DC suburbs) which was licensed to Colonial Beach but eventually crept closer to the “big city” of Fredericksburg, VA. They were able to locate on a tower very close to the city...problem was, they didn’t technically cover their COL with a 60dBu signal. They tried to use L-R coverage to justify their move — the FCC told them to either move back to a closer tower to Colonial Beach or figure out a new COL. They did the latter, of course...adding a new 100w non-comm station to ensure the good folks in Colonial Beach didn’t lose their only licensed service (yet to sign on).
I can attest that while WGRQ was licensed to Colonial Beach, and on the new tower...once you started going down the hill into the town, WGRQ did not cover that area with a city grade signal at all.