If you're talking about TCP connections, after the connection has established client and server are equivalent, both are free to send data as long and as much they like and/or shut down their end of the connection.
Edit: After several passes I think i have understood what the second paragraph of your question is aiming for.
There is, of course, nothing which would stop the server from doing anything.. What your server seems to do, most of the time, is blocking on a InputStream.read() operation. If you want the server to operate even when no network input happens, one solution might be to use a read timeout, or check the input stream for readability before actually reading.