Washington (CNN) With Deputy Attorney General Rod Rosenstein possibly on his way out , a fresh round of uncertainty has been injected into the Russia investigation, and it could take a while for things to settle down.

Typically, a special counsel would answer to Attorney General Jeff Sessions. But he recused himself last year amid controversy about his meetings with the Russian ambassador during the campaign. With Rosenstein out, the Justice Department's succession plan comes into play.

The Justice Department says the next man in line is Solicitor General Noel Francisco , a Trump appointee who was confirmed by the Senate by a 50-47 vote along partisan lines. Francisco is a conservative lawyer who worked in the Bush administration and was also active in the private sector.

But the federal government's former ethics czar disputed this succession plan Monday, as news about Rosenstein was breaking. Walter Shaub, who ran the Office of Government Ethics and is now a CNN contributor, wrote on Twitter that Francisco can't take over the probe "unless the White House has secretly issued a waiver" of an executive order that Trump signed last year.

That order says federal appointees can't participate in matters related to their former employers and clients for two years. Before joining the Trump administration, Francisco was a partner at the law firm Jones Day, which represents the Trump campaign in the Mueller probe.

Whoever takes charge of the Mueller investigation could decide that it's time to wind down the probe or dismiss Mueller altogether. The person in charge of the investigation would have the power to reject indictments and other investigative requests, including whether to refer investigations to other federal prosecutors.

Over the past year, Rosenstein has largely backed Mueller's known requests to bring criminal charges against two dozen Russians and a handful of Trump associates. He also supported requests to refer cases to other federal prosecutors, like with former Trump lawyer Michael Cohen. The new person in charge could draw a much harder line, complicating Mueller's job.

Any swift action against Mueller by a new appointee would almost certainly raise red flags, because Trump has mused in the past about firing Rosenstein to put a check on Mueller. If there is "corrupt intent" -- like ousting Rosenstein as a means to kill the Russia probe -- his firing could factor into Mueller's obstruction of justice investigation.

Democrats are sure to renew their calls for legislation to protect Mueller's investigation, which has been largely rebuffed by Republicans on Capitol Hill. Top Republicans have voiced support for Mueller but said there is no need to pass any bills because he isn't going to get fired.

Regardless, if Mueller's new boss shows him the door, that doesn't mean the investigation would automatically end. Many of the dozen or so lawyers working for Mueller would still be DOJ employees and the cases they're working on — especially the ones open before federal judges -- would not disappear overnight.

With Francisco next in line, DOJ ethics officials would check to see if he has conflicts preventing him from overseeing Mueller. If he has a problem, the next person to fill Rosenstein's shoes would be Steven Engel, who is an assistant attorney general for the Office of Legal Counsel.

The Mueller investigation has progressed for 16 months, resulting in indictments against 35 defendants, including some top Trump officials. With large swaths of Mueller's cases now involving other US attorneys' offices and the Justice Department's National Security Division, Rosenstein's replacement might not have as much influence in the direction of the sprawling investigation.

Perhaps the biggest remaining questions are whether Mueller will seek a subpoena for Trump's testimony, which would require formal signoff from his boss at DOJ, and what to do if the investigation determines Trump broke the law during the campaign or as president.