When a radio (subscriber) comes up on a talkgroup at a site, it has affiliated. Basically the subscriber is telling the system "Hey I'm here at Site X, and I want to listen to TG Y", at which point the system will start broadcasting that TG's radio traffic at that site. If the subscriber de-affiliates and there are no other subscribers at that site on that TG, the traffic is no longer carried.
There are exceptions to this rule, but they require the system admin to force traffic to be carried regardless of subscriber affiliation (or lack thereof) and are not commonly done.
So the bottom line is that if there are no radios requesting talkgroups at your local site, there won't be anything to listen to. The system is operating normally, and the site is not "disconnected" from the rest of the system.