dying gasp notifications – alerts generated by a device when it is about to reboot, reset or otherwise go down.
If a device is able to issue a dying gasp, either from software via SNMP, syslog or using a specific external interface then it helps to diagnose the problem. In some equipment, when the power fails to that device it has enough residual power (perhaps using an Ultra capacitor or similar) to issue a message indicating that the power has failed.
This is most useful for service providers who are putting small edge devices into many locations such as the cabinet at the end of your street. If the device can issue a dying gasp for power failure, then the NOC knows that device power has likely failed and it is probably not a circuit failure or a hardware failure or similar. In this case, a dying gasp means that they can wait a while to see if the power comes back on before dispatching a team to fix the device thus saving money.
Now a standard feature for a lot of telco equipment.