Without closing the socket:
The difficult problem isn’t the BufferedReader.readLine, but the underlying read. If a thread is blocked reading, the only way to get it going is to supply some actual data or close the socket (interrupting the thread probably should work, but in practice does not).
So the obvious solution is to have two threads. One that reads the raw data, and will remain blocked. The second, will be the thread calling readLine. Pipe data from the first the second. You then have access to a lock than can be used to wakeup the second thread, and have it take appropriate action.
There are variations. You could have the first thread using NIO, with a single thread instance shared between all consumers.
Alternatively you could write a readLine that works with NIO. This could even take a a relatively simple single-threaded form, as Selector.wakeup exists and works.