So far I've only found one beggar that I can click on and give them coin to get them to stop asking for more help. That was in Shorehelm.
Can ZOS devs do this for the rest of the beggars so we can get them to stop them from repeating their 'requests' over and over every time we pass by them? Gets depressing after a while.
If the devs can get npcs to cheer us every time we enter the city that we saved, putting in something to 'help' the beggars should be doable too.