Improved full example and added pkill-P version.

all-full-example.sh

@@ -1,7 +1,6 @@
 #!/bin/sh
 set -e
 
-# From https://stackoverflow.com/a/360275
 kill_child_jobs() {
     echo "In kill_child_jobs()..."
     # Workaround for https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=482999
@@ -45,7 +44,7 @@ done
 trap cleanup EXIT
 
 yes aa &
-yes b &
+yes disowned & builtin disown || true
 sleep 100 &
 
 wait

pkill-P-full-example.sh

@@ -0,0 +1,28 @@
+#!/bin/sh
+set -e
+
+kill_child_jobs() {
+    echo "In kill_child_jobs()..."
+    # From https://stackoverflow.com/a/23336595
+    # Kills all child proceses, not just jobs.
+    pkill -P $$
+
+}
+cleanup() {
+    kill_child_jobs
+}
+
+# From https://unix.stackexchange.com/a/240736
+for sig in INT QUIT HUP TERM; do
+  trap "
+    cleanup
+    trap - $sig EXIT
+    kill -s $sig "'"$$"' "$sig"
+done
+trap cleanup EXIT
+
+yes aa &
+yes disowned & builtin disown || true
+sleep 100 &
+
+wait