We have investigated the magnetic properties of CuNCN, the first nitrogen-based analog of cupric oxide CuO. Our muon-spin relaxation, nuclear magnetic resonance, and electron-spin resonance studies reveal that classical magnetic ordering is absent down to the lowest temperatures. However, a large enhancement of spin correlations and an unexpected inhomogeneous magnetism have been observed below 80 K. We attribute this to a peculiar fragility of the electronic state against weak perturbations due to geometrical frustration, which selects between competing spin-liquid and more conventional frozen states.