The electronic structure of the lightly electron-doped correlated spin-orbit insulator Sr2IrO4 has been studied by angle-resolved photoelectron spectroscopy. We have observed the coexistence of a lower Hubbard band and an in-gap band; the momentum dependence of the latter traces that of the band calculations without on-site Coulomb repulsion. The in-gap state remained anisotropically gapped in all observed momentum areas, forming a remnant Fermi-surface state, evolving towards the Fermi energy by carrier doping. These experimental results show a striking similarity with those observed in deeply underdoped cuprates, suggesting the common nature of the nodal liquid states observed in both compounds. [ABSTRACT FROM AUTHOR]