Sorry to hear that aman,,
I switched TV with my Benq monitor(which has no HDMI CEC/ARC control), and turned off the HDMI control from both Firestick and AV Receiver. In my case when I switch off the monitor, music get paused immediately and If I press the play button again, music start playing.
So I did some digging and what I found out is, after switching off the monitor, the lights on the LAN port(My firestick is connected through LAN) went off and lights back on when I press the I play button. That's mean If the firestick don't find any display it goes back to standby mode.
Unfortunately you can't turn off the auto standby feature on firestick. It's really annoying.
So I think there are two options
1. Just turn off the display of your TV.(If you have the features)
Or
2. Just press the play button again when the music paused..
Try it and tell us how it goes. Or if you find any better solution please let us know.