Mrs.LL and I have had long discussions on this. She has vastly more restaurant experience than I do, but we're both pretty familiar with the practice. And while there are no "rules"--everything is just an ad-hoc determination--there are some patterns that you can discern.
Soups, pastas, and other dishes in which the customer is going to have to dip a fork or spoon that s/he is continually eating off of back into the food--that shit is right out.
Pizza, sandwiches that the kitchen cuts in half before it hits the table--if there's a whole slice of pizza or a whole half a sandwich that is left behind, that's absolutely free game.
French fries, chips, and other things that get handled one-at-a-time--yeah, those are generally free game. But cold french fries are gross. And the reality is that the customer's hands are rummaging through that pile of fries/chips/fried whatever, and that's kind of gross. But at the same time, if you're a college student, eating a fried shrimp that someone's hand brushed past is far from the grossest thing you're going to do today, soooo . . . .
Things like half a steak or a chicken breast that the customer would've used a knife to cut slices away with the fork only touching the piece that is being cut away and going straight into the mouth (leaving the remaining portion of the steak untouched by any mouth-touching utensil)--this is a real gray area. If there's the filet half of a prime porterhouse that's left sitting on a plate untouched, I'm eating it. No question.
The gold mine is the to-go box that the customer leaves behind.