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1.
Like a startup business, but one that fails to start. The process of ending a startup.
Joe, how's your new startup business coming?

We couldn't get any VCs to back the idea in the end, so we've turned it into a finishup, and I'm looking for a job.
by rickbrunernyc April 20, 2010
 
2.
Finishing food from a previous meal. Similar in description to that of leftovers. In fact, basically the same. However, no one else seems to use this slang.
Enrico: What are you having for dinner tonight Jose?

Jose: Just some finish ups from last night.
by Banyos February 09, 2011