A brain gain with a brain drain.

"We study human capital depletion and formation in an economy open to out-migration, as opposed to an economy which is closed. Under the assumption of asymmetric information, the enlarged opportunities and the associated different structure of incentives can give rise to a brain gain in conjunction with a brain drain. Migration by high-skill members of its workforce notwithstanding, the home country can end up with a higher average level of human capital per worker."