A lot consequences, especially for the civilians. It depends on what nations are next to the country. Usually, when the number of refugees grow, countries will let them come in their boundaries.
With more refugees, population for the country will decrease. However for the refugees, they will have horrible journeys and it will be really hard for them to get a residency in the place.
They will be looked down on in the country and wont have much money to support themselves. Over-population is bad for countries so they within time, more refugees will be shut out. A lot of death, and worser treatment for the refugees.