What is this braided line going through the drain trap?

That line is almost certainly a trap primer setup, though it looks unusual because it's integrated into the drain structure itself. What you are seeing is a way to maintain the water seal in the P trap, even when the main sink is not in use, or in a scenario where the drain might not have enough continuous flow. The idea is to supply a small amount of water directly into the drain loop to keep it full. Since commercial facilities, especially high-rise public washrooms, are subject to strict building codes regarding drain maintenance and odor control, they often use these systems. It prevents the trap from drying out completely between uses, which would allow sewer gases to escape.

In a typical residential setup, the P trap is kept sealed by the weight and flow of the water going down the drain, but in high-traffic public spaces, the usage patterns are inconsistent. A sink might be used heavily for an hour and then not used again for four hours. Without continuous flushing, the water in the trap could evaporate or be siphoned out by other environmental factors, compromising the seal and causing smells. The primer keeps that specific section of the drain constantly supplied with liquid.

I have seen these mechanisms installed specifically for floor drains or utility sinks where usage is intermittent, but adapting it into the main sink drain line is a common modification in newer commercial builds to ensure the building stays compliant with all sanitation standards. It’s a bit of extra plumbing complexity, but it guarantees the trap remains operational and sealed.

It's a functional detail driven more by code compliance and maintenance concerns than by a specialized faucet feature. It's essentially a constant refill loop ensuring the water seal is never broken.

Spot on diagnosis. I've run into these a lot doing fit-out work in office towers, probably touched a dozen of them in the last couple years. One thing to add: a lot of these don't drip constantly, they're triggered by usage elsewhere. Flush a nearby toilet and the pressure change sends a little burst of water down into the trap. That's why the routing looks so wierd, the line has to reach back to whichever supply feeds the fixture that activates it. If you ever hear a faint gurgle or trickle from that sink after someone uses the next stall over, that's the primer doing its job.

That makes sense of somethig at my work actually. The handicap stall sink there smells funky every Monday morning but fine the rest of the week, so I'm guessing its trap is drying out over the weekend since barely anyone uses it. So with one of these primer setups, does it still trickle water in even when nothing else in the building is running, or does it only work when other fixtures get used?

To answer the weekend-stink question, most of these primers only fire when something else in the building gets used, since they piggyback on the pressure drop from a flush or a valve opening somewhere downstream. That's exactly why a lightly-used sink is the classic failure case, and it sounds like your Monday sink is a textbook example. The alternative is a continuous drip type that feeds constantly, but those are the less common flavor around here. On the supply side, my basement floor drain primer kicks in every time the washing machine dumps its discharge, which took me a while to figure out because I kept looking for a leak before I understood what the little braided line actually did.

Ran into the same thing on a job at a small clinic a few years back. The exam room sink basicly never got used and the smell was awful every time I walked in. Ended up pulling the old setup and putting in a trap primer tee on the tailpiece and that was the end of the odor issue. Wish I'd known about them sooner, woud have saved me from chasing phantom leaks that turned out to be nothing. Funny how a part most homeowners have never heard of just quietly solves a problem they'd swear is a venting issue.

Update: trap primer makes total sense now that you say it piggybacks on pressure changes from other fixtures. That explains why it looked like it was wired into the drain. One thing still bugging me though. If it only fires when a toilet flushes somewhere nearby, what happens in a wing of the building that's empty for days, like over a holiday weekend? Does the trap seal just dry out anyway before anyone uses it again?