A fat wreck is a person, usually someone who is heartbroken or fucked up over a relationship, who has eaten their feelings, usually a large amount of junk food, and perhaps alcohol, and has reached the terminal capacity for food, and has no choice except to examine themselves, and the wreckage of chip bags, pizza boxes and beer cans littering their domicile.
A fat wreck can also be a large wreck, or a big mess.
"Man, what happened to you? Why is our apartment a disgusting mess?"
"Linda broke up with me, man. I'm a fat wreck."
OR,
"That ten car pile up on the freeway was a fat wreck. Traffic was terrible."