Reaver nails it. Namikaze also makes good points, though I'll add one alternative to staying on the run is to build connections with the poor and destitute in said techo's area. Spreading around a little money and a little food can go a long way to making a hellhole a good place to hang your hat -- assuming you remember to pick it back up before you head outside.
I'm less inclined to go the taxation route. That runs the risk of turning murder hobos into accountants with guns, and while I hate murder hobos, I'm more likely to want to play in that game than the latter.
I also feel that there is an assumption that the techo is out to game the system. That may well be true, but it's a dangerous assumption to make. Let's go with the bias against technos as a thought experiment. One could make the argument that a techno living a Middle Lifestyle would be faced with a greater chance of being abducted, killed, or extracted than one living in a squat, or on the street. If a run against a corp gets said techno's face on video feed, that can be cross-referenced with the cameras that will undoubtedly litter the middle lifestyle areas, and then it's just a matter of time before someone sees which apartment building s/he enters and makes a move. Living in the Barrens, though? Chummer crosses over from Bellevue, and s/he's gone. Chummer makes nice with the local hoods, poses as a decker who will hack in Urban Brawl for the neighborhood to watch, and otherwise keeps his nose down, and he stands a relative shot at peace. Not only that, but s/he's playing the char in 1 of myriad "right" ways to do so. Technos don't need those fancy gadgets, so if the techno is looking for a way to spend some hard-earned ¥, doesn't want to leave the streets, and is playing up the slightly off and unusual cliches for the archetype, I say go for it. That's RP gold. The OP said the player in question approached to talk about how to spend some money; I don't see why the only answer is to improve the lifestyle, when it's possible to effectively raise one's lifestyle -- including the expenses that come with it -- while RPing the char in a way that the player wants to.
Also, if you really want to tax the player, and make him/her think twice about living on the street, just have a random hood try to mug the PC. Maybe the PC gets lucky, and runs off, or bests the thug, but s/he'll certainly think twice about walking around with 25k. And if the PC doesn't doesn't get off that lightly, well hard lesson learned.