Puking hard food

My boyfriend's cat has a constant filled bowl of indoor cat food. Almost every day I find puke that looks like poop but is hard food, not much fur. I don't think it's hairballs because there's not much fur, but I don't think it's eating too fast because she always has food

That sounds a lot like a cat I had. If this is a life long issue I recommend (but see below) going to the vet, asking if there's a test for a weak stomach valve...that keeps food in the stomach. I think that was my cats issue.
You might be able to test this theory by holding cats front half up for about 15 minutes (if possible), or putting her food bowl on a little two tiered kind of shelf so that her head and stomach are raised.

It's also possible it's the food itself....have you tried switching to canned food, or buying something like the Catch Feeder, designed to slow down fast eaters. And actually, I might try something like this first, unless the cat seems to be malnourished or ill, because barfy cats and dry food is actually kind of common, unfortunately.
http://northmate.com/category/products/catch/