DocuSign Admins could locate Envelopes through Reports for any DocuSign User but that will not provide access to the envelope document. You must create a share to that User's envelopes to locate and review that Users sent envelopes.
As I understand it the envelopes can be purged but I do not know of an Archive feature in DocuSign. Unless you close the account or the Sender/Recipient deletes the envelope the envelope is within DocuSign forever, you just need to make sure the filter applied to any Search is set appropriately to include older timeframes. Current filters go back only 6 months by default.