Burnt relay what caused this

This looks like a run capacitor to me. How about telling us the make and model number of your appliance.

An electrical issue usually is what causes the run capacitor to malfunction. When the PTC doesn't correctly indicate the refrigerator's temperature, the run capacitor won't know when to turn on. It could turn on too frequently or not at all. When the capacitor is not working properly, usually you'll hear a clicking sound either before or after the compressor turns on. When you're checking whether the run capacitor is working properly, you can use a power meter to gauge how much energy is being passed between the PTC and the run capacitor. Your owner's manual should tell you the amount of energy that should be passed if it is functioning properly.

UPDATE

Here’s your part:

WPW10662129 - Whirlpool Refrigerator Capacitor

Capacitors fail, it’s just a fact of life. The capacitor can fail because the motor is getting old and takes more to start, surge/voltage spike (either from the line or bad motor's back-emf), or just it failed/life expectancy was reached. ... Capacitors (similar to light bulbs) will fail at some point.