“coughing up tree-shaped clots?” I have not heard of this. Do you have more information? This sounds awful.
Here’s one from 2018:
https://www.techentice.com/heart-patient-coughs-up-bronchial-tree-like-blood-clot/?amp
I met a man a few months ago who had such a clot removed from his trachea, he said. He described it to me. He told me about the Physician who removed it. She was a young Dr. of Asian descent. This procedure happened in my hospital. We talked about it some. He told me what Unit he was in and what the view outside of his window was like.
It was definitely my place. He wanted to show me a picture of it,(the clot) but he was unable to find it. It seemed far fetched to me because there is no way that he would have been alert and oriented so soon following such a thing. He insisted though. I did not know that Physician who did it, but that is not unusual.
I have seen images before, but I never met a Patient with such an experience. I was uncertain regarding the veracity of this story. I simply cannot know.
It clearly would have been fatal in a short time if what described was accurate and truthful, if it were allowed to progress.