Hello, my name is***** and I have over 20 years of veterinary experience. I am sorry to hear that your fellow Gunnar ingested a bar of soap.
All soaps are gastrointestinal irritants and can lead to drooling, vomiting and diarrhea with a loss of appetite. We do not recommend inducing vomiting in cases of possible ingestion as that only leads to further irritation of the esophagus. Of course I understand you didn't induce vomiting, but rather the irritant effects of the soap led to his vomiting. What that means however is that his stomach and esophagus are very, very irritated.
I'm not surprised he hasn't passed any stool with the amount of vomiting he has done. There isn't likely anything left to make stools.
In most cases the gastrointestinal juices break the soap into small enough pieces to pass, rarely would we see an obstruction from a bar of soap.
Is he drooling or continuing to vomit?
There are some things you can do at home today to ease his stomach and gastrointestinal irritation.
To try and settle his stomach you can try either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle his stomach and decrease the burn from the soap and repeated vomiting. These should be used for several days as necessary as they are quite safe and will aid in healing.
Then if he stops vomiting and seems less nauseous feed a homemade diet of 1/3 boiled, very lean hamburger or boiled, white, skinless chicken, all fats drained off the meat, and 2/3 boiled, plain, white rice.
Add 2 to 4 tablespoons of canned pumpkin, (not pie filling, just pumpkin), to each meal for fiber to help push the chunks of soap through his gastrointestinal tract and ease irritation. Feed small meals several times a day.
Once he's feeling better then start mixing in his regular food, adding a little more regular and less bland at each meal. It should take a week to get him converted back to regular food.
If he continues vomiting, even after the acid reducing medication is given, refuses to eat or has explosive diarrhea it is best he see a veterinarian for an examination, injectable medications and oral medication like sucralfate to coat his gastrointestinal system.
Let me know if you have any questions.