Ejection of core electrons as a result of recollision in a laser-driven carbon atom is theoretically investigated with a quasiclassical model. The model, called "fermionic molecular dynamics," gives rise to a ground-state carbon atom where the six electrons are paired in shells, with different binding energies. This feature renders possible, on a classical level, the discussion of the ejection of electrons from different shells. By analyzing a large number of trajectories of a carbon atom exposed to an intense, few-cycle laser pulse, we reveal a class of recollision trajectories where the recolliding electron is recaptured into the atomic core after ejecting a core electron. We also discuss the difference between quadruple ionization trajectories leading to a final C 4+ ion where the two bound electrons have opposite spin, and the trajectories where the bound electrons have equal spin.