This happens occasionally with steak for me. What I've done is take a gulp of air like kids do when trying to force a burp. First time I tried that, the piece of steak literally sounded like a cork popping off a bottle when it fired down out of my esophagus into my stomach. I have done that twice now, it works way quicker than trying to soften the food with water or soda and constantly spitting up the liquid.
i think you'll find better answers at a different forum i'm pretty sure the people on this forum are concerned about gastroenterology anyway it doesn't matter. By the way the way bread and water are a big help if you know its still there after a couple of hours, start hitting his back in an un-painful way if possible because he might cough it up. Or doing a handstand works. Either way this is not a hospital situation the body can't leave with a piece of meat stuck in its throat it'll do something on its own
Also sometimes it "feels" like it is still there and really is not. But in these cases people can drink water.
You really need to see a doctor about this regardless of out come. Only eat soft foods until then. As some people get older (much older) their esophagus can narrow. It is correctable, not that hard. They inflate a balloon thing in there. My uncle had it done at 90 yrs old.
If this was just a mistake because someone didn't chew and swallowed it by mistake, it is still an ER visit if it is still suck after 1 minute because the esophagus can start to swell. I am only thinking of worst case situation, but anything stuck is not good.
If the food is jammed in the esophagus and won't go down I'd think that is an emergency situation. If it came back up from gas it could cut off his air way, and if he can't drink he will become dehydrated. I'd go to the ER.