The solution, it would seem, is to help those who want to emigrate emigrate and let those who want to stay stay, and let the country slowly die on the vine.
Have you seen the population graphs for Russia[0] vs the USA[1]? It seems like one of the only developed countries (besides Japan) with a decreasing population. Seems like that is happening already.
[0] https://www.google.com/search?q=population+of+russia
[1] https://www.google.com/search?q=population+of+usa