Ok, so in Undertale, ghosts are invulnerable, and can’t be killed.

When you try to kill Napstablook, they just say this:

When trying to attack Mad Dummy, he says basically the same thing.

But after he fuses with his body in the genocide run, you can kill him easily.

So when ghosts become corporeal, they also become mortal. When their body is destroyed, they die.

so, as a ghost, Mettaton was immortal, but has fused with his body and can now die.

Mettaton literally gave up immortality for nice legs