The publication by the Commissioner of a resolution for dissolution shall not impair any right of a depositor or creditor to payment in full of his lawful claims nor impair any right or remedy theretofore had for the enforcement thereof, provided, however, that all debts and demands for the recovery of which no action shall have been commenced against the dissolving bank on or before the termination of six years from the first day on which the publication was made by the Commissioner shall be barred and unenforceable after the termination of said six year period, and no action shall thereafter be commenced therefor, and further, provided, that this section shall not extend the time or limitation on any action that would otherwise be earlier barred.