Yup, not all slices work out perfectly. Waste bits that get a little overcooked, bits that are too crumbly to slice well, overly fatty bits-- those all get chopped and tossed into a pot to simmer and reduce a little bit, render a little more of the overly fatty part, and put on a sandwich as "chop" or "chopped beef." Down here in Texico, depending on the joint, that might get sauced, or it might not, and traditionally it was thrown onto a hamburger bun, to make a "chop beef on bun."
These days here in CenTex, more people really like those fatty slices and they actually command a premium over lean, so less of it goes into chop than before.