We study the Brownian dynamics of flexible and semiflexible polymer chains densely grafted on a flat substrate, upon rapid quenching of the system when the quality of solvent becomes poor and chains attempt collapse into a globular state. The collapse process of such a polymer brush differs from individual chains, both in its kinetics and its structural morphology. We find that the resulting collapsed brush does not form a homogeneous dense layer, in spite of all chain monomers equally attracting each other via a model Lennard-Jones potential. Instead, a very distinct inhomogeneous density distribution in the plane forms, with a characteristic length scale dependent on the quenching depth (or equivalently, the strength of monomer attraction) and the geometric parameters of the brush. This structure is identical to the spinodal-decomposition structure, however, due to the grafting constraint we find no subsequent coarsening: the established random bundling with characteristic periodicity remains as the apparently equilibrium structure. We compare this finding with a recent field-theoretical model of bundling in a semiflexible polymer brush.