Why does my cat keep biting the back of other cats necks?

My mom and her 4 (ugh) cats have moved in with me and my one cat almost a year ago. There were some understandable issues with the cats at first but they seamed to have settled themselves out. But just this last month, my cat kept biting the neck of this one cat. Then the cat had to be put to sleep because he had a stomach tumour. And now my cats found another cat to bother. We thought with the other cat gone he'd stop but nope. Is there some reason he HAS to be picking on someone? They don't even get into fights or bother him to warrant a bite. They'll just be walking by or sleeping and he'll bite their neck.