I have no special skills in interpreting strace outputs but this would
appear to be confirmation that cups-browsed cannot contact cups when it
closes down.
cupsd _is_ running. The strace fragment simply shows cups-browsed trying to connect to
IPv6 localhost, port 631 (over and over). It can't connect because my cupsd doesn't listen on localhost:631 (neither IPv4 nor IPv6), only on a domain socket (/var/run/cups/cups.sock).