To explain my question I tried doodling the scenario. Keep in mind I've been digging into TCP on my own so the diagram might not be too reliable. Please let me know if this is so.
Question:
What happens if a client that has an open connection with a server over TCP does not ACK a FIN sent by the server (seen at #1)?
Possible Answers:
The FIN will be sent again, exactly as for a data segment, subject to the same retry counters and timeouts.
If the client wants to keep the connection open after the server sent FIN can the client do anything to tell the server to keep it open? i.e. Ask for some more data.
No. Once a host has sent a FIN it cannot send any more data. However the peer can send in the other direction, unless the host has actually closed the socket.