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Van der Waals layered chalcogenophosphates, such as CuInP₂S₆ and AgInP₂S₆, exhibit intriguing polar properties such as room temperature ferrielectric ordering, negative electrostriction, large elastic nonlinearity, proximity to ionic conductivity and multi-well ferroelectric potential, presumably due to a unique influence of the van der Waals gap. Here we will discuss anomalous properties of domain walls in ferrielectric selenophosphate CuInP₂Se₆ detected using piezoresponse force microscopy. Whereas in ferroelectrics, including a structurally similar case of ferrielectric CuInP₂S₆, electromechanical response and polarization vanish at the domain wall, the reverse is true in the case of CuInP₂Se₆, so that piezoresponse vanishes everywhere but the domain wall. And yet, these domain walls can be manipulated by electric field. We propose the existence of an antiferroelectric phase in the near-surface layer of CuInP₂Se₆, with locally enhanced polarization at antiferroelectric domain walls. Nature Comms. in review (2019).