Hello,
This is my first time of asking a question.
What is the effect of privatization on unemployment

It depends country to country. In Pakistan, where there is over employment in nationalized firms, when they are privatized, the over employed force is fired. So in this way Unemployment increases due to privatization.

Welcome, are you discussing the effect of making the US unemployment system a private system. ( private insurnace) If so I have never thought about it, but it could be possible.