© 2018 American Physical Society. A strong gravity naked singular region can give important clues toward understanding the classical as well as spontaneous nature of General Relativity. We propose here a model for energy emission from a naked singular region in a self-similar dust spacetime by gluing two self-similar dust solutions at the Cauchy horizon. The energy is defined and evaluated as a surface energy of a null hypersurface, the null shell. Also included are scenarios of the spontaneous creation or disappearance of a singularity, the end of inflation, black hole formation, and bubble nucleation. Our examples investigated here explicitly show that one can model unlimitedly luminous and energetic objects in the framework of General Relativity.