Deception. Moving a piece on a game board should have more than one effect. One should preferably make it so that the most obvious effect (exile) is not the one that's actually the most valuable in the long term (taking root in adverse country).

Bonus "inception" points if you can make the adversary believe that you did it because they forced you to (sanctions).

For example, you wholeheartedly support the policy, but are not comfortable living under the sanctions.

My understanding of Exile is that you are rejected by the society you are exiled from, due to your actions or beliefs. Like profound disagreement with the policy.

I have certainly seen the kind of people you talk about, they support (or at least used to) Putin, but don't want their kids to live in Russia. I would call them more like emigrants of convenience.