Monte Carlo simulation of annealed copolymers of solvophobic/solvophilic monomers show collapsed globular states having dynamic core-shell structures. In these, the core is mostly solvophobic while the core boundary contains an excess of solvophilic monomers. This two-state model, where each monomer undergoes interconversion between solvophobic and solvophilic state, is a minimal version of models of neutral water-soluble polymers such as PEO. The reduced surface tension of such core-shell structures suggests an explanation of the stability of PNIPAM globules as observed in the experiments of Wang et al. [Wang, X.; Qiu, X.; Wu, C. Macromolecules 1998, 31, 2972]. The statistics of the monomeric states along the chain vary with the degree of chain swelling. They are differ from those of quenched copolymers designed to create water-soluble globules though both systems involve a core-shell structure.