We experienced something kinda related.
A cat that was unwell... multiple trips to vet who could not work out what was wrong. Cat was gradually losing its fur as well. A animal skin specialist unable to diagnose exactly what was up, though some sort of poisoning/ reaction to something eaten seemed likely. As it was ongoing, specialist began quizzing the vet as to what medicines he had prescribed. Meanwhile, cat Cerys was getting sicker, losing weight and lots of her fur

To cut a long story short, after some time, amongst latest cat sick, I found a LARGE rubber band (flat wide type).. which the cat had apparently swallowed some time back. Some sort of allergic reaction to the chemicals in that was the cause. The specialist agreed.. in fact I had to package up the sick and rubber band for him to analyze. He did say he was writing a scientific paper on the whole event.... I never heard any more about it, but maybe he did and my cat Cerys is famous in scientific circles?