In this paper, we investigate the boundary feedback stabilization of a quasilinear hyperbolic system with zero characteristic speed and a partially dissipative structure.This structure enables Health Monitors us to construct a Lyapunov function that guarantees exponential stability for the H2 solution.We also introduce another set of stability conditions by restricting terms corresponding to zero eigenvalues to the dissipative part, which still ensures exponential stability.As an application, we achieve feedback stabilization for the modified model of neurofilament Floss Products And Dental Tools transport in axons.