Giving the impression of a dying device - making a vibrating motor slow down and stop
You can control the motor using PWM (Pulse Width Modulation) and make it run for full, then slowly decrease the speed till stop and after light up the led.
This tutorial from Adafruit could be a good start if you are not familiar with PWM and have also some good advices: https://learn.adafruit.com/adafruit-arduino-lesson-13-dc-motors/overview

Please be really careful about the supply source. Motors can easy draw more current then the limited available from the pins of arduino. Maybe a H-bridge could be helpfull here.(take a look at this for example of h-bridge: https://learn.adafruit.com/adafruit-raspberry-pi-lesson-9-controlling-a-dc-motor/lm293d )