To have a fallthrough case with the bash case statement you simply use ;& instead of ;; in the case you want to have fall-through behavior, so as follows:

case $VAR in
    normal)
        echo "This doesn't do fallthrough"
        ;;
    fallthrough)
        echo -n "This does"
        ;&
    fallthrough)
        echo "fall-through"
        ;;
esac