What is this component?

From the picture it seems it’s only a cosmetic damage, that’s a coil part of the ethernet circuitry and it seems in order. If you can try if the ethernet works fine you would have a confirmation. In case it’s damaged it would likely prevent ethernet proper functioning but it’s not a critical component and shouldn’t probably be regarded as a possible culprit for shutdowns. It can be fixed by replacing it if needed by some shop into component level repairs. Random shutdowns with that model are probably due to a fault in graphics circuit.