How can Catholics who adhere to Eucharistic Miracles claim the distinction between substance and accidents?

The question of “are Catholics cannibals due to their view on transubstantiation” question cropped up quite some time ago. The top [answer](https://christianity.stackexchange.com/a/30327/56226) on this question makes a distinction between substance and accidents. >In other words, if the wine becomes the Blood of Christ, why isn't there hemoglobin in it? > >Aristotelian philosophy made a distinction between what (in modern philosophical jargon) is called "substance" (from Latin substantia, the essence or nature of something) and "accident" (from Latin accidens, something that happens to be true of an entity). Aristotle of course used Greek, but Aquinas used the Latin. The substance of something is what makes it what it is: I am a human being because I am human "in substance"; that is, because I have "humanness". I look the way I do as a human because I have particular accidents—my eyes are a given color, my hair and skin, I'm a given height. Any of those things could change, or could have been different; that would change what I looked like, but not what I am (i.e. human). > >The Catholic teaching on the Eucharist is that during the Eucharistic celebration, the substance of the bread and wine—what they truly are—is changed into the substance of the body and blood of Christ. But their accidents—what they look and act like physically—remain the same. So I have a question. I’ve seen many cases of Eucharistic miracles, that is, where traces of real blood are found in the consumed Eucharist. Many people claim this as evidence of transubstantiation. But how does this fit with the substance vs accidents view? Because wouldn’t a Eucharistic miracle be a change in accident, not substance? Beyond that, do proponents of Eucharistic miracles think this happens all the time, or is it a rare occurrence? And if it is a rare occurrence, are these cases cannibalism?