The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability for classes of square-summable sequences with Z-transform vanishing at isolated points with a mild rate; the case of non-summable sequences is not excluded. The transfer functions for recovering algorithm are presented explicitly. Some robustness with respect to noise contamination is established for the suggested recovering algorithm.