We have reinvestigated the Si $2p$ photoemission spectra of a clean $\mathrm{Si}(001)c(4\ifmmode\times\else\texttimes\fi{}2)$ surface with an apparently higher resolution than previous studies. A systematic and extensive line-shape analysis of the spectra taken at various photon energies and emission angles indicates that the Si $2p$ spectra are composed of seven different components. With regard to the recent debate on the Si $2p$ component of the down-dimer atoms, we conclude that even with the present resolution the corresponding surface core-level shift (SCLS) cannot be determined accurately but is in the range of 30--130 meV between the bulk and the second-layer components. One of the two newly identified components, with a SCLS of 1.4 eV, is interpreted as a surface loss structure due to the interband transition between surface-state bands.