From the Athens News

THE INTERIOR ministry announced on June 17 that non-European Union nationals in Greece who are in the process of renewing their residence permit may travel to their homeland this summer as long as they leave after June 20 and return before September 19.

Immigrants will be allowed to re-enter the country on or before September 19 if they have a document (veveosi) verifying they have submitted an application to renew their residence permit.
As is the case each year, bureaucratic delays in the renewal of permits would have forced tens of thousands of immigrants in Greece to spend their summer holiday separated from friends and family in their homeland.

Immigrants with valid permits may travel abroad and re-enter Greece any time they wish.

Happy Holidays.