Don't pull. Sorry

Some folks call those flags. I have helped [gently] to eliminate these flags, from a dog in the past. I'd be very careful and if ya hold on the dog may pull away from you at his own rate to pull it out.

dont pull if he cant push it out himself do not pull...you cant know if a string is wraped around any where......call the vet or watch and wait...it sounds like he is able to push it out himself...but not knowing how long or how much their is a worry.....do you know it is? a sock? a piece of towel?

i know you may think this odd but for the next two days,,,,,make sure you SEE your dog poop normale...yes that means watching and then going over to check it....you want to make sure a) that he is pooping and their is no more cloth.....
remember dogs rip and pull thigs apart...so you may have only seen a few of the pcs and their stuff still left.....
i had a dog poop one sock i thought everthing was ok....wrong the other sock was stuck!!!!! big bucks time to get it removed.....
so keep watching for anymore fabric.....and vomiting brown smelling bile....hunched up...go see the vet.....

The rest seems to be in his normal feces. It seems to be part of a blanket or cloth of some kind.

that these 'strings' can be twisted around some of his guts! You don't know what it is that he swallowed, or how shredded it has become, and these threads can be stubbornly strong and get twisted or knotted somewhere in this colon (the rectum being the last part of the colon)so you can cut it off, or you can gently hold it and see, with very little pressure, whether it will easily release...but don't pull. Dogs have been known to eat long things like pantyhose, that can stretch!