With more than one client connected at a given time, if you want to stop the backup server (e.g. to shutdown, or to do disk maintenance or whatever), then you can't because init.d/boxbackup-server will only kill one PID, not all of the connected clients.  This means that if you operate on the backup store believing it inactive you can corrupt data.  In addition it means client connections are terminated uncleanly when shutting the system down, if there is more than one client connected at a time.

Even if this isn't grave it's serious, because failing to stop processes (IIRC) associated with a init.d start script is a violation of "Debian Policy".

severity 633930 important
retitile 633930 /etc/init.d/boxbackup-server should terminate open connections
stop

I haven't verified this behavior, but the description makes sense to
me. Additionally to shutting down the service, the init script should
also terminate running connections.

Which part of Debian Policy are you referring to?

To me, this issue does not seem serious enough to immediately work on it
nor to pull it out of the next release.