After sending the STOP signal to a process, it stops working as expected, but still accepts TCP connections. So is it working anyhow?
Once a Unix process binds an IP address and port to a stream socket, the kernel begins accepting TCP connections for that address/port and continues until the socket is unbound or closed. The process gains access to the connections via the accept() system call, but the connections are happening regardless. Beyond the initial TCP handshake, the connection is idle until accept() is called and the process start to use the connected socket.
So connections are occurring but there isn't any real activity (mail being sent, web pages being served, etc.) while the process is stopped.