Thank you for your question. My name is***** I have been a small animal veterinarian for 13 years and I'd like to help with your question.
It can be stressful whenever a dogs eats something that he shouldn't. Was it just the prongs that he ate? So the pieces were not more than maybe a little larger than an inch? There is a good chance that they will pass with minimal difficulty. There is also a chance that they might cause some trauma as they pass or even get stuck somewhere along the way. You have a few choices.
Since the pieces are no in the stomach- making him vomit to try to get them out is an option. If it is successful and he vomits it up, then the problem is solved, however there are a number of risks to this approach. First, there is the possibility that it could get stuck in the esophagus on the way back up and cause him to choke or just lodge somewhere that is very difficult to access to remove it. Second, he could aspirate and develop pneumonia from the vomiting. I have had dogs successfully vomit up things they have swallowed, but I don't think it is worth the risk in this case.
The second option is that a veterinarian can retrieve the plastic from the stomach with surgery or an endoscope. This is probably the safest option. The stomach is the safest part of the intestine to do surgery on. The down side is the expense. Surgery to remove the rawhide might run you $1500 or more and endoscopy would be the about the same. There would be a short hospital stay and recovery period, but this option offers the fastest safe resolution to the problem.
The third option is to feed him high fiber diet and hope that the plastic can bend and twist it's way through the intestine and pass. I have seen this happen too.... it just depends on how thing move in there. If it passes you are all good, but if it gets stuck then you have to go to surgery to retrieve it. And the surgical cost and complication of removing it from the intestine once it is stuck will be higher than removing it from the stomach now. With small foreign bodies this is a possible option, watch him closely. The first sign of belly pain or vomiting and you need to head to surgery.
I hope this helps, but if you have additional questions please let me know. If not, please rate my answer.