I don't think Rosenstein is going anywhere, in the foreseeable future. Trump could fire him, as he could with other appointees, but this would clearly look like obstruction. With Rosenstein's involvement in the Russia probe, and since Sessions has recused himself, it's unlikely Sessions could fire him either. So, if the firing is to take place, it would have to be through a congressional impeachment process. That's not gonna happen either. This is my understanding of the situation and I could be wrong. I'll reiterate...Rosenstein isn't going anywhere.