The operating system will automatically close all TCP connections when a process exits1.
What you are seeing is probably a connection in the TIME-WAIT state ("...represents waiting for enough time to pass to be sure the remote peer received the acknowledgment of its connection termination request").
This should not be a problem for clients, as a host can establish multiple TCP connections to the same remote host:port.
For a server, SO_REUSEADDR can be used.
This socket option tells the kernel that even if this port is busy (in
the TIME_WAIT state), go ahead and reuse it anyway. If it is busy,
but with another state, you will still get an address already in use
error. It is useful if your server has been shut down, and then
restarted right away while sockets are still active on its port. You
should be aware that if any unexpected data comes in, it may confuse
your server, but while this is possible, it is not likely.
It has been pointed out that "A socket is a 5 tuple (proto, local
addr, local port, remote addr, remote port). SO_REUSEADDR just says
that you can reuse local addresses. The 5 tuple still must be
unique!" by Michael Hunter (firstname.lastname@example.org). This is true, and this
is why it is very unlikely that unexpected data will ever be seen by
your server. The danger is that such a 5 tuple is still floating
around on the net, and while it is bouncing around, a new connection
from the same client, on the same system, happens to get the same
remote port. This is explained by Richard Stevens in ``2.7 Please
explain the TIME_WAIT state.''.
See also this StackOverflow answer: Using SO_REUSEADDR - What happens to previously open socket?
1 Technically, when all handles to that connection are destroyed. Multiple processes may own a file handle.