What blood thinners are given to people with a heart attack/stroke and gastritis/ulcers?

Risk vs benefit: In life (& in medicine), everything we do is a balance of what benefit we hope to gain vs. what risk we have to take. The correct treatment for someone who has had a heart attack or stroke (in the long term) is aspirin. That comes with a small risk of bleeding. Coated aspirin, especially the 81 mg strength) is unlikely to aggravate gastritis or stomach ulcer since it dissolves lower down.