How can I log the stdout of a process started by start-stop-daemon?

It seems you should be able to use now the --no-close parameter when starting start-stop-daemon to capture the daemon output. This new feature is available in the dpkg package since version 1.16.5 on Debian:

Add new --no-close option to disable closing fds on --background.

This enabled the caller to see process messages for debugging purposes, or to be able to redirect file descriptors to log files, syslog or similar.

You need to do:

start-stop-daemon --start --quiet --chuid $DAEMONUSER    \
    --make-pidfile --pidfile $PIDFILE --background       \
    --exec /bin/bash -- -c "$DAEMON $DAEMON_ARGS > /var/log/some.log 2>&1"

Also if you use --chuid or --user, make sure the user can write to /var/log or the existing /var/log/some.log. The best way is to have that user own a /var/log/subdir/ though.

To expand on ypocat's answer, since it won't let me comment:

start-stop-daemon --start --quiet --chuid $DAEMONUSER    \
 --make-pidfile --pidfile $PIDFILE --background       \
 --startas /bin/bash -- -c "exec $DAEMON $DAEMON_ARGS > /var/log/some.log 2>&1"

Using exec to run the daemon allows stop to correctly stop the child process instead of just the bash parent.

Using --startas instead of --exec ensures that the process will be correctly detected by its pid and won't erroneously start multiple instances of the daemon if start is called multiple times. Otherwise, start-stop-daemon will look for a /bin/bash process and ignore the actual child process running the daemon.