Is it possible for a person to never fart?

Sounds like Ogilvie’s Syndrome. In residency I saw a man who had had an infected total knee joint replacement removed; he was on strict bed rest for several days and his belly got bigger and bigger each day, to the point that his breathing was compromised as well. Unfortunately, his upright chest film showed free air in his abdomen; his colon had perforated. During surgery, no mechanical obstruction was found - it was strictly a dysmotility problem. I don’t recall whether he survived.

Ogilvie syndrome is typically treated by decompressing the colon, either by medical stimulation of the colon or by mechanical decompression with a colonoscope or suchlike. One of the old docs I knew recommended ‘The Position’, in which the patient was placed on hands and knees, head down, butt up in the air. After a few minutes of this, many patients relaxed to the point that they’d start to decompress in a looooooooooooooooooong, low, whistling toot. The problem being, that most of the patients who developed Ogilivie’s couldn’t tolerate getting into that position due to incisions, pain, etc.