Last modified: 2013-11-01 14:51:20 UTC
The Countdown extension should have an option to display a "finish message" when the target date/time has been reached (i.e. 0 seconds, or negative seconds, remaining). See https://www.mediawiki.org/wiki/Extension_talk:Countdown#Request This should be implemented as a tag parameter, e.g. <countdown time="12/31/2015 5:00 AM UTC-0500" finishmessage="We're done">. The tag will display either that finish message or what it usually renders, viz. days, hours, minutes, seconds, etc. remaining.
It's unmaintained, so likely WONTFIX.