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Most neutron stars (NSs) and black holes (BHs) are believed to be the final remnants in the evolution of massive stars. In this study, we propose a new formation channel for the formation of BHs and peculiar NSs [specifically, magnetars and Thorne–Żytkow objects (T$\dot{\rm Z}$Os)], which we refer to as the core-merger-induced collapse (CMIC) model. This model involves the merger during a common-envelope phase of an oxygen/neon/magnesium composition white dwarf and the core of a hydrogen-rich or helium-rich non-degenerate star, leading to the creation of peculiar new types of objects. The results of binary population synthesis simulations show that the CMIC channel could make important contributions to the populations of (millisecond) pulsars, T$\dot{\rm Z}$Os, magnetars, and BHs. The possibility of superluminous supernovae powered by T$\dot{\rm Z}$Os, magnetars, and BHs formed through the CMIC model is also being investigated. Magnetars with immediate matter surroundings formed after the CMIC might be good sources for fast radio bursts.