The recent update to the dns-root-data package in jessie changed its format which in causes dnsmasq to not be able to start up, which causes DNS servers running dnsmasq to not work.
See debian bug # 858506 for more information for when this happened on stretch. The attached patch is taken from there and fixes the issue. Nick Hall
--- etc/init.d/dnsmasq.orig 2018-07-02 07:09:55.553073068 -0500 +++ etc/init.d/dnsmasq 2018-07-02 07:10:36.385072508 -0500 @@ -111,7 +111,7 @@ ROOT_DS="/usr/share/dns/root.ds" if [ -f $ROOT_DS ]; then - DNSMASQ_OPTS="$DNSMASQ_OPTS `sed -e s/". IN DS "/--trust-anchor=.,/ -e s/" "/,/g $ROOT_DS | tr '\n' ' '`" + DNSMASQ_OPTS="$DNSMASQ_OPTS $(cat $ROOT_DS | tr '[:blank:]' '\t' | cut -f4- | sed 's#^[A-Z]\+\s\+## ; s#^#--trust-anchor=.,# ; s:[ \t]\+:,:g' | paste -s -d ' ')" fi start()