It is shown that phagraphene, a recently predicted planar allotrope of graphene with Dirac fermions, is unstable or, at least, almost unstable with respect to transverse atomic displacements. This result is obtained by numerical calculations in the framework of both the tight-binding model and the density functional theory. A nonplanar atomic configuration of phagraphene has a wavy shape and is almost degenerate in energy with the planar configuration. The main types of possible structural defects in phagraphene are determined. The temperature dependence of characteristic times of their formation is found.