How can Communism exist with government?

You are referring to the "fantasy" end state that all communists use as propaganda to get their minions to do their bidding. No "real" communist state has ever reached the fabled "end state". The states we call communist are those whose avowed goal is to reach that end state "some day". Of course in reality the whole thing was just a con to get power. Much like the lies that Obama told to gain power was a big con.