According to the Comptroller General in a recently published bid protest decision, there is nothing improper about such an activity.
...the protestor argues that the agency's extension of the closing date for receipt of initial proposals was improper because it occurred after the initial closing date has passed. This assertion fails to state a valid basis for protest because there is no prohibition against a procuring agency issuing an amendment to extend the closing time for receipt of proposals after that time has passed to accommodate even one offeror, where the motivation for the extension is enhanced competition.The key here is that the post-closing date extension must be motivated by a desire to "enhance" competition. If there was only one bidder, that might be justified. If there were multiple bidders however, that justification may not fly. Hopefully, Government contracting organizations have sufficient controls in place where such extensions must be approved by upper management so as to preclude improper practices.
You can read the entire bid protest decision here.