How much Karma could a player expect to drain with this power from npcs? Every other form of energy drain has a cap: people only have so much essence, and everyone has it. They presumably have karma as well, but how much?

How did the player get the karma drain power? Is this some horrifyingly out of balance thing from 5th ed? Cuz there aren't any player options in 4th ed that give it.

Anyway, most NPCs don't have karma. That's a player thing. Some named NPCs like Harelquin for example, do have karma held in reserve but I wouldn't imagine a player would have much luck draining it from someone that powerful.
The GM can just choose how much karma a given NPC has and tell the player when he has drained it all. Perhaps 1d3 would be a good number to use.
Honestly though, this is a pretty over powered thing to give a player.

Power Pact with a Free Spirit that has the power. Street Magic in 4th edition.