How did this object p through my dog?

My one year old lab had been acting sick for the last 3 days or so. He had diarrhea, vomiting, regurgitation, and lethargy. I made him a vet appointment for today. But, this morning I found a large (size of a dish towel) piece of a braided rug on the floor. I am sure that he either vomited it up or pooped it out. It was covered in a brownish/green slime and left similarly colored liquid stain on my carpet (yuck!!). I was wondering how you think he ped the piece of rug, through vomit or poop? He is acting like his old self. I am not certain if I should cancel my vet appointment or not? Probably all questions for my vet. However, I am just curious what the community has to say. Thanks.