Something like Dust skips the backward pass on backprop. But other techniques like Neural Predictive Coding can be completely asynchronous, each "weight" can fire independent of those far away from it. Innocenti, et. al have shown that NPC gradients converge to backprop within a certain "regime".

The win with asynchronous techniques like NPC is that you do not need the extreme co-ordination that backprop requires and hence should be computationally much easier given the right device.

Although at this point the industry has so much money in the forward-backward pass system that I doubt a backprop successor would win unless someone makes NPC hardware feasible and can prove scaling up to billions of params