LD_PRELOAD this as a library to output a binary's output from syslog() on stderr as well as any syslog daemon that's listening (useful for Docker, if you want all log output to be collected by Docker's standard output handling.) Beware though, if the program changes its stderr file descriptor (closes it, points it at /dev/null, pipes it out to a socket), this can have surprising results. For example, when I tried this with cyrus-imapd, I was getting syslog output sent to remote clients because stderr and stdout were remapped that way (not maintaing the original fd that Docker set up.)
COPY syslog2stderr.c /build
RUN gcc -fPIC -shared /build/syslog2stderr.c -o /usr/local/lib/syslog2stderr.so
RUN echo /usr/local/lib/syslog2stderr.so >> /etc/ld.so.preload
RUN gcc -fPIC -shared /build/syslog2stderr.c -o /usr/local/lib/syslog2stderr.so -ldl
... was needed that it worked for me. Thank you!