We report the dewetting of a thin polymer bilayer on a low surface energy topographically patterned substrate with grating geometry. The bilayer, comprising of a polystyrene (PS) top and poly(methyl methacrylate) (PMMA) bottom layer was prepared by direct sequential spin coating on the patterned substrate, using mutually exclusive solvents. Depending on the coating conditions, three distinct initial morphologies of the as coated bilayer is possible: type I, a discontinuous bottom layer under a discontinuous top layer, resulting in polymer threads confined within the substrate grooves; type 2, discontinuous threads of bottom layer polymer (PMMA) confined within the substrate grooves under a continuous top layer; type 3, continuous bottom and top layers. Our experiments reveal that the initial morphology of the film, particularly, that of the bottom layer significantly influences the final dewetted patterns. For example, in a type 1 or type 2 bilayer the morphology depends significantly on the relative widths of the PMMA threads (LT-PMMA) and that of the substrate grooves (L-p). In case LT-PMMA < L-p, the bottom PMMA layer disintegrates into isolated droplets aligned along substrate grooves, irrespective of the thickness or morphology of the top PS layer. On the other hand, the overall morphology of the dewetted film is rather strongly influenced by the thickness of the PS layer and the configuration of the bilayer. In case the PMMA threads span the entire width of the substrate grooves (LT-PMMA = L-p), the droplet formation is suppressed in favor of an intact PMMA thread, with periodic undulations, submerged under either an undulating thread or an intact layer of PS. In case of a type 3 bilayer, the continuous PMMA bottom layer in most cases ruptures over the substrate stripes, where it is thinnest. This result in the top PS layer coming in direct contact with the substrate and subsequently rupture over the same locations, resulting in core shell threads localized over the substrate grooves. In case of a type 3 bilayer with an ultrathin top film, the two layers rupture simultaneously at different locations and subsequent dewetting results in an exotic structure comprising alternating array of PS droplets and undulating PMMA threads. For a thicker bottom layer, the PMMA film is seen to remain intact, over which the PS film dewets, forming undulating threads. We also construct a morphology phase diagram that depicts the influence of the individual layers on the final dewetted morphology.