President Trump has refused to rule out the notion of pardoning former National Security Adviser Michael Flynn, infuriating Democrats like Sen. Mark R. Warner, who said this week that the pardon of a key witness or meddling with the special counsel investigation would cross “red lines.”

But presidential pardons have become somewhat common in the wake of special counsel investigations resulting in criminal charges.

In five out of the six most recent independent or special counsel investigations in which criminal charges were brought, presidents eventually issued pardons or commuted sentences. At least 12 such investigative teams have convened over the past 25 years, and the other half of cases were closed without criminal prosecution.

Mr. Flynn has pleaded guilty to lying to the FBI. Special counsel Robert Mueller secured the plea as part of his ongoing investigation into Russian meddling in the presidential election last year and suspected coordination with members of the Trump campaign.

Although Mr. Trump has said he is not planning to fire Mr. Mueller, he has expressed concerns with the way the investigation has been run and prompted speculation that he could be considering a pardon.

Asked last week about the possibility of a pardon for Mr. Flynn, Mr. Trump said he didn’t want to talk about the scenario “yet.”

“We’ll see what happens. Let’s see,” Mr. Trump said.

Legal analysts say there is a distinct difference between granting a pardon amid an ongoing investigation, as is the Russia probe, and granting one after the conclusion of the case.

“What would be highly unusual would be if President Trump were to pardon people in the middle of the investigation,” said Richard Painter, who served as White House ethics counsel under President George W. Bush. “Pardoning in the middle of an investigation raises the specter of wanting to influence witness testimony.”

He said such a move could be seen as trying to influence witness testimony, which could leave the president open to obstruction of justice charges, Mr. Painter said.

Mr. Flynn’s plea agreement indicates he is cooperating with the Mueller probe. Another campaign adviser has also agreed to plead guilty to making false statements to investigators, and two high-level Trump campaign associates are fighting the charges.

“A pardon shouldn’t be used to try and hide the truth. The pardon should be used because the president believes the punishment was too harsh. And if it’s used early, particularly in an investigation that involves the White House, I think people will say it’s being used to hide the truth,” Mr. Painter said.

Mr. Warner, the ranking Democrat on the Senate Select Committee on Intelligence, voiced similar concerns on the Senate floor this week to push back against “the growing chorus of irresponsible and reckless voices” calling for the dismissal of Mr. Mueller.

“It is up to every member of this institution, Republican or Democrat, to make a clear and unambiguous statement that any attempt by this president to remove special counsel Mueller from his position, or to pardon key witnesses in an effort to shield them from accountability or shut down the investigation, would be a gross abuse of power and a flagrant violation of executive branch responsibilities and authorities,” the Virginia Democrat said.

Mr. Trump’s quick pardon of former Maricopa County, Arizona, Sheriff Joe Arpaio had Democrats wondering whether he would take similar action in the case of Mr. Flynn. Mr. Arpaio was appealing his July contempt of court conviction and didn’t have a finalized judgment against him when Mr. Trump issued the pardon in August.

The president has used his clemency powers one other time, this week, by commuting the sentence of a kosher meatpacking executive.

The Arpaio pardon has proved controversial. Some Democrats even went to court to argue that it subverted justice and should be ignored. The judge rejected those arguments.

Mr. Painter noted that President Ford waited until after investigations had run their course and the Watergate “smoking gun” tape had come to light before pardoning former President Richard Nixon.

But some presidents have issued pardons early.

Weeks before leaving office, President George H.W. Bush pardoned six former officials in the Reagan administration who faced charges as part of the Iran-Contra investigation, including former Defense Secretary Caspar W. Weinberger, who was set for trial.

The move infuriated independent counsel Lawrence Walsh, who at the time said the decision “undermines the principle that no man is above the law.” He focused on Mr. Weinberger’s pardon in particular, saying it completed the Iran-Contra cover-up.

Eleven people pleaded guilty or were convicted by juries as part of the investigation, though some convictions were reversed on appeal.

The most recent clemency in a special counsel case was granted in 2007, when George W. Bush commuted I. Lewis “Scooter” Libby’s 30-month prison term.

Vice President Dick Cheney’s chief of staff had been convicted of obstruction of justice and lying to investigators looking into the leak of a CIA operative’s name.

President Clinton, meanwhile, issued pardons to at least one person in each of three cases brought by special counsels.

In a final batch of pardons issued hours before he left office in 2001, Mr. Clinton cleared former Housing Secretary Henry Cisneros; several people charged as part of Kenneth W. Starr’s Whitewater probe, including his former Whitewater business partner Susan McDougal; and several men convicted in connection with the investigation of former Agriculture Secretary Mike Espy, who had been acquitted.

Investigators who work for special counsels are aware that their prosecutorial efforts could be overturned by presidential pardons, said Andrew Leipold, a law professor at the University of Illinois who served as a consultant on Mr. Starr’s Whitewater investigation.

“But what do you do about it?” he said. “The pardon power is too unpredictable. Lots of presidents’ friends have been indicted on lots of things and probably thought they were going to get pardons and didn’t.

“Are you aware of it? Of course,” Mr. Leipold said. “But I don’t think you do anything different.”

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