First, whoever fires Mueller might eventually just replace him with someone to finish the investigation. After all, there are several indictments outstanding that need to be tried; plea agreements that need to be finalized; and open investigative leads. In the “normal” course of business, if the lead prosecutor leaves an investigation, he just gets replaced. That might happen here—especially since the political pressure to replace Mueller would be fairly intense. This, after all, is what happened after President Richard Nixon fired special prosecutor Archibald Cox—Leon Jaworski was appointed.

Second, since the investigation would still be open, we might see the investigation continue but without a special counsel. That’s partially what has already happened with respect to the investigation of Trump’s attorney, Michael Cohen. That investigation is now being handled by the U.S. Attorney’s Office in the Southern District of New York—a regular unit of the Department of Justice. If Mueller were fired, the ongoing pieces of his investigation (into Manafort, Russian social-media interference, etc.) could also get farmed out to various U.S. attorneys’, or a Department of Justice, litigating division to pursue. If that happened, the investigations might lose some coordination, but they would continue apace.

Finally, and most problematically, whoever fired Mueller could also order that the investigation be closed out.