The stuff they part-ingest then throw up on my office floor would seem left over. Or left behind.
Dogs do that with poop quite often.
But no, it's not left over/behind. It's just "tasty but indigestible". (Think sugarfree gummi bears or similar for us humans. Taste really nice, but make your insides go brrrröööööt if you eat more than three in one sitting.)
The things cats and dogs find "tasty" never ceases to amaze me, their taste buds are just so wildly different to us humans.
Some things we share – cooking meat, like sizzling bacon in particular –, but others differ so much I have hard time even imagining it.
Cats don't really taste sweet/sugar at all, for example.
It's a funky experience to alter ones taste temporarily with e.g magic berries (
synsepalum dulcificum) that cause us humans to taste everything sour as sweet instead. (It contains a
glycoprotein that temporarily (for up to an hour) binds to our taste buds.)