Signals ignored by a shell cannot be handled by its sub-shells?

[Clark J. Wang]

For example:

[bash-4.2.8] # cat a.sh
trap '' TERM
bash b.sh
[bash-4.2.8] # cat b.sh
echo "Now in $0 ..."
trap sig_TERM TERM
sig_TERM()
{
    echo "got SIGTERM, exiting ..."
    exit
}
kill -TERM $$
sleep 1
echo "Not killed?"
[bash-4.2.8] # bash a.sh
Now in b.sh ...
Not killed?
[bash-4.2.8] #

-Clark