Can anti-clotting drugs benefit an elderly person who has a second stroke?

Yes, if an embolus. Strokes can be caused by clots that form in the heart and travel to the brain, most often if the person has atrial fibrillation. In this case, anti-clotting drugs definitely reduce the risk of another. If the stroke was caused by bleeding, they should not be used. Strokes can also be caused by small vessel diseae, and they are not helpful for these.