A lot of wastelanders are suffering dehydration and need purified water, which when given to them rewards the Lone Wanderer with positive Karma (+50). Denying them water causes them to die at the next map change, even if they were given purified water before. However, telling them to find their own water, and then giving them water is fine, and they live on. They do not die if you do not explicitly tell them to find their own water, however, and their death inflicts no karmic penalty on the player character.
Giving them Aqua Pura with the FEV will incur -50 Karma.
Strangely, they never actually drink the water you give them and it can be pickpocketed back.
Ben Canning, a wastelander who appears in a random encounter, can be given purified water or dirty water in exchange for good Karma as well. In his case, repeating the action is not possible which is why he is not considered part of this unmarked quest.
Even though the beggars are apparently too weak to get water for themselves, they have no problem getting up and running away from a potential conflict.
Individuals can be heard saying that the beggars are scammers and trick people into giving them money.