So it mean I can pay 0 fee everytime I send BTC and it still get confirmed one day?
It is entirely possible. So long as a transaction is broadcast, there is always the possibility for it to be confirmed.
So how to STOP broadcasting it?

You can't. You can have your wallet stop broadcasting it (either remove the transaction from your wallet or just shut down the wallet), but you have absolutely zero control over what anyone else on the network does. Someone else on the network could be broadcasting it, you can't do anything about that.
Your only option to "cancel" the transaction is to create a double spend which spends the same input but to an output that you control.