Type Iax supernovae (SNe Iax) form a class of peculiar SNe Ia, whose early phase spectra share main spectral line identifications with canonical SNe Ia but with higher ionization and much lower line velocities. Their late-time behaviors deviate from usual SNe Ia in many respects; SNe Iax continue showing photospheric spectra over several 100 days and the luminosity decline is very slow. In this work, we study the late-time spectra of SN Iax 2019muj, including a newly presented spectrum at ∼500 days. The spectrum is still dominated by allowed transitions but with a lower ionization state, with possible detection of [O i]λλ6300, 6363. By comprehensively examining the spectral formation processes of allowed transitions (Fe ii, Fe i, and the Ca ii near-IR triplet) and forbidden transitions ([Ca ii]λλ7292, 7324 and [O i]), we quantitatively constrain the nature of the innermost region and find that it is distinct from the outer ejecta; the mass of the innermost component is ∼0.03 M
⊙ dominated by Fe (which can initially be 56Ni), expanding with a velocity of ∼760 km s−1. We argue that the nature of the inner component is explained by the failed/weak white-dwarf thermonuclear explosion scenario. We suggest that a fraction of the 56Ni-rich materials initially confined in (the envelope of) the bound remnant can later be ejected by the energy input through the 56Ni/Co/Fe decay, forming the second unbound ejecta component which manifests itself as the inner dense component seen in the late phase.