  We study the fate of a collapsing star on the brane in a generalized
braneworld gravity with bulk matter. Specifically, we investigate for the
possibility of having a static exterior for a collapsing star in the radiative
bulk scenario. Here, the nonlocal correction due to bulk matter is manifest in
an induced mass that adds up to the physical mass of the star resulting in an
effective mass. A Schwarzschild solution for the exterior in terms of this
effective mass is obtained, which reveals that even if the star exchanges
energy with the bulk, the exterior may appear to be static to a braneworld
observer located outside the collapsing region. The possible explanation of the
situation from the discussion on the role of bulk matter is provided. The
nature of bulk matter and the corresponding bulk geometry have also been
obtained and analyzed, which gives a complete picture of both brane and bulk
viewpoints.
