The Kamioka Liquid scintillator Anti-Neutrino Detector is used in a search for single neutron or two-neutron intranuclear disappearance that would produce holes in the s-shell energy level of C12 nuclei. Such holes could be created as a result of nucleon decay into invisible modes (inv), e.g., n→3ν or nn→2ν. The deexcitation of the corresponding daughter nucleus results in a sequence of space and time-correlated events observable in the liquid scintillator detector. We report on new limits for one- and two-neutron disappearance: τ(n→inv)>5.8×1029 years and τ(nn→inv)>1.4×1030 years at 90% C.L. These results represent an improvement of factors of ∼3 and >104 over previous experiments.