Can oral digestive enzyme supplements harm the stomach? can abruptly stopping them after prolonged use have downsides?

No, and maybe: If you are talking about Creon or one of the generic equivalents (pancrealipase, etc) then those supplements are not going to harm your stomach. They are copies of your digestive enzymes anyway. Stopping them could cause gas and distention and intestinal problems (as you may not digest your food properly - if you have pancreatic insufficiency - your pancreas not making enough of those enzymes).

Yes at times,only if: Most digestive enzymes have protease which can irritate your stomach if it's inflamed.Those with ulcers & gastritis can be irritated by such enzymes.There's no harm in abruptly stopping but if you need enzymes for digestion you'll suffer from lacking them.You can get products like SGI by Theramedix that have fat & starch digesting enzymes without proteolytic enzymes,designed to soothe the stomach.