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 ^(12)C 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 × 10^(29) years and τ(nn→inv) > 1.4 × 10^(30) years at 90% C.L. These results represent an improvement of factors of ~3 and > 10^4 over previous experiments