Can emigration slowly kill a country? That's apparently what some people think. Aside of Bulgaria, there is also Hungary that has a real emigration problem and even the "tiger state" of Romania.
The problem is, of course, manifold. The opening up of the labour market towards central europe, the non-existence of modern market reforms and a political instability that is the legacy of a long soviet and despotic reign. All of them have an increasing GDP/person ratio:
So there is a silver lining after all. This bodes well for the private sector, but the falling population rates spell doom for public retirement schemes. These public expenditures in the future might mean that harsh cuts await future retirées. And yet I believe even though population levels are decreasing, the agile markets in those countries could save them if given the freedom necessary.
Given enough time and a more stable law and order environment, all three countries might regain their footing. People usually don't quit countries easily and many hang on to their homeland for a long time, even reconsidering going back.
Of course, you can only capture those people, if they see the opportunity to come back and live a decent life again. This means that wealth creation should be the top priority of those governments.