Yes. Let's say I'm X, with channels to A and Z. If A usually receives payments, like LOOP and some exchanges, I tend to charge a high fee rate towards A. And, because the sats tend to flow towards A, I have to do some trickery (like rebalancing) to keep enough sats on my side.

With negative inbound fees (from A to my node X) I can encourage the rest of the network to use the edge A->X because it makes the whole payment cheaper. If the destination is Z, the negative fee rate A->X reduces the overall fee one has to pay for A->X->Z. If, for example, I charge 1000ppm for X->Z and set a negative inbound fee rate of -200ppm for A->X, the total route A->X->Z only costs 800ppm instead of 1000ppm (plus whatever A charges to reach my node X, but this cost is the same with or without negative inbound fees).

Progress: #527580