I will describe certain exotic property of Gromov boundaries, called pro-π₁-saturation, which holds for a class of word hyperbolic groups called 7-systolic. The class is related to the idea of simplicial negative curvature introduced by T. Januszkiewicz and myself. The property says that every closed subset in the boundary is π₁-injective in this boundary, in certain shape-theoretic sense. This excludes 2-disc from being a subset of the boundary. 7-systolic groups are the only known ones with boundary of (topological) dimension above 2 and pro-π₁-saturated. Nevertheless, I suspect this property to be generic (in some not yet discovered sense) among high-dimensional Gromov boundaries of groups.