Does the body eat fat when starved?

Yes it does. The body starts digesting its own fat. Once that runs out, then the body may start breaking down muscle tissue and other tissues.

After so much starvation, there comes a point where it is irreversible since the protein synthesis centers are made out of protein. So once enough of these "protein factories" are destroyed, the cells in the body continue to starve, destroying the means to make energy from protein.