One would like to assume that extra food would be made available in an area that's most relevant to that department's employees; I think they should certainly have first dibs.  But, if it's not eaten, I don't think that it should be thrown away; make it available to whoever might enjoy it.

Years ago I was an Assistant Food Services Director for Aramark.  Aramark is a contract company.  I worked in the Business Dining Division.

When departments have meetings food purchased comes out of their budget.  In essence, you're asking, "If my neighbor goes to the store, pays for deli items and has leftovers on the counter, can I have them?"

The leftovers are usually left within the department as a courtesy to those members.

I say yes it is in a public area, but at the same time I would ask who ever i was talking to just so i was not "that guy". I work in an office where we put the food out after a meeting for all and it is like attack dogs half the time begging for scraps. I also think some people smell the food is out and just show up.