What code is executed when headphones are disconnected?

In most systems if not all, ACPI can handle this event. To test that:

1. Run acpi_listen

2. Unplug & replug headphones, example output: (mic/ears share in same jack on my laptop)

   jack/headphone HEADPHONE unplug
   jack/microphone MICROPHONE unplug
   jack/headphone HEADPHONE plug
   jack/microphone MICROPHONE plug
   

3. Put your-script.sh in /etc/acpi/

4. Add an event trigger file for your script in /etc/acpi/events/

   event=jack/headphone HEADPHONE unplug
   action=/etc/acpi/your-script.sh
   

   Check the other files there to learn from.

5. You may need to restart acpid service to reload changed rules in /etc/acpi/events/

   sudo service acpid restart
   

Reference: man acpid

The current version of your script now contains a sleep 0.25 command.

sleep is timer-based so doesn't use any processing cycles while sleeping…

It does use a very tiny bit of CPU to set up the timer, but sleep 1 (sleep 1 second), sleep 60 (sleep for a minute) and sleep 86400 (sleep for a day) all use the same number CPU cycles.

Using ACPI however is the perfect solution as ACPI is event-driven instead of polling-driven.