  The paper investigates recoverability of sequences from their periodic
subsequences and offers some modification of the approach suggested in papers
arXiv:1605.00414 and arXiv:1803.02233. It is shown that there exists a class of
sequences that is everywhere dense in the class of all square-summable
sequences and such that its members can be recovered from their periodic
subsequences. This recoverability is associated with certain spectrum
degeneracy of a new kind.
