Clubs can have station licenses on a case-by-case basis. They are getting a lot more rare. Any correspondence about them usually would go directly to the trustee. These days, most club stations are the same as a ham's callsign. But there are others, like KL7KC in Fairbanks which are grandfathered in order to keep the callsign. In any case, it is up to the trustee to keep things in order. So this kind of letter wouldn't usually be addressed to the station location. KL7KC is in a CAP hanger which is rarely manned. There would be no expectation of a quick response if a letter was to be sent there.
Station licenses are definitely used for broadcast stations, and are tied to a specific location. The FCC maintains a separate tower database the correlates stations with tower locations, too. You need a station license and construction permit before you even begin to build a broadcast tower.
Ham licenses go with the person, not the location.
This question is a tad misleading, but it is the correct answer the way the question is asked. The second part, suspension of the operator license, is possible.
The reality is, the only reason this would apply to a ham is if they have been accused of a violation of some sort.
I have been a ham since 1971 and have never received anything like this from the FCC.
I have been a broadcast engineer since 1979 and have seen many kinds of letters from the FCC show up that required my attention. The station managers involved are always in a hurry to respond asap.
When I earned my General Radiotelephone Operator License back in 1983 it was required that I post it at stations where I was the engineer of record. (Back then the announcers all needed Third Class Radiotelephone Operator Licenses, too). But things are a lot different now.