7.2 Debian claims to be able to update a running program; how is this accomplished?

The kernel (file system) in Debian GNU/Linux systems supports replacing files even while they're being used.

We also provide a program called start-stop-daemon which is used to start daemons at boot time or to stop daemons when the kernel runlevel is changed (e.g., from multi-user to single-user or to halt). The same program is used by installation scripts when a new package containing a daemon is installed, to stop running daemons, and restart them as necessary.