A simple majority in the House can impeach a civil officer of the government; 2/3 majority in the Senate can then remove.
I don’t see 2/3 of the Senate voting to remove Rosenstein, but if a simple majority does, that would be political cover for Trump to fire him.
“I must confess that Im ignorant of the procedure. I fully understand the impeachment and removal process for the elected Executive Branch members and the Judicial Branch. But not of appointed officeholders. I had always assumed they were just fired.”
Your comment makes me wonder if this will make it easier for Trump to fire the guy?
https://www.senate.gov/artandhistory/history/minute/War_Secretarys_Impeachment_Trial.htm
So, honestly, is it possible that lightning could strike twice? Pretty doubtful; there is senate procedure to retain jurisdiction over a former official, but honestly, I don't see this going anywhere.