Bash script on background: how to kill child processes

Well, I'm basically trying to make a bash script runs a node script forever. I made the following bash script:

#!/bin/bash
while true ; do
        cd /myscope/
        unlink nohup.out
        node myscript.js
        sleep 6
done & echo $! > pid

I'm expecting that when it runs, it starts up node with the given script, checks if node exits, sleeps for 6 seconds if so and reopen node. Also, I'm expecting it to run in background and writes it's pid (the bash pid) on a file called "pid".

Everything explained above works as expected, apparently, but I'm also expecting that when the pid of the bash script is killed, the node script would stop running, I don't know why that made sense in my mind, but when it comes to practice, it doesn't work. The bash script is killed indeed, but the node script keeps running and that is freaking me out.

I've tested it in the terminal, by not sending the bash script to the background and entering ctrl+c, both scripts gets killed.

I'm obviously miss understanding something on the way the background process works. For god sake, can anybody help me?