It would require some serious coding, but I'm sure it can be implemented.
You would have the option of displacing an 'alien' community from one of your cities, and for each 2 pop of these 'aliens' a single 'refugee' unit would be represented, which the displacor would be able to do one of several things to:
a) Exterminate - this creates a -3 modifier with its native civ and any civs friendly to it, while destroying the 'refugee' unit.
b) Move the unit elsewhere in the invading civ's empire and add it to another city (adding 2 pop to that city in addition to bringing some of its native culture, although this would diminish if outside of the native civ's sphere of cultural influence over time), incurring a -1 diplomatic modifier with the native civ solely.
c) Take the refugee unit to the border with another civ and offer it to them. Benefits for taking in refugees would include a 2 pop boost and a +2 diplomatic modifier with the native civ. Disadvantages would include taking on some of the native civ's culture in the city the refugees join, in addition to 15 turns of +1 angry face due to tension caused by immigration. The invading country who forced this emigration would suffer a -2 diplomatic modifier with the native civ, while incurring a -1 diplomatic modifier with the civ that accepts the refugees.
I'm sure there are plenty of other facets to the refugee unit that could be hammered out...game balance and wider gameplay effects would be priorities when thinking about those changes to the unit, but I'm frankly too tired to work further on the idea (it's 2am here). This does seem modable, if a challenge - so if we're content with a finished product this might become a suggestion for a modder extraordinaire.
Not sure about the numbers involved in the effects...would a -6 modifier for exterminating 2 Refugee units be a game-breaker? If you think so, suggest alterations to the numbers involved - again I apologise, I'm very tired so a bit of thought on that would certainly be appreciated.