On login/connection, join an existing tmux session. If none exists, create one. If creating a session fails, drop back to the user's shell. Otherwise, if there weren't any errors, disconnect the user.

.bashrc

# Automatically connect to (or establish) a tmux session
## if we are in a TTY and we aren't in a tmux session and we aren't connected through a gui...
if ( [ -t 1 ] && ! [ -n "$TMUX" ] && [ -z "$DISPLAY" ] ); then
	## Attach to tmux, if we fail, start tmux.
	## On success, exit the ssh connection.
	## On failure, give the user a warning and drop them to the shell
	tmux a || tmux
	if [ $? -eq 0 ]; then
		exit
	else
		echo "Warning: Unable to connect to tmux, falling back to the normal prompt"
	fi
fi