Washington Redskins left tackle Trent Williams and tight end Fred Davis are expected to miss the remainder of the NFL season as punishment for multiple failed drug tests under the terms of a settlement between the league and the NFL Players Association, according to people with knowledge of the deal.

Both players, cornerstones of the franchise and two of its top contributors this season, played for a final time this season in Sunday’s 34-19 loss to the New York Jets. The NFL is expected to formally notify Williams and Davis early this week that they must serve four-game suspensions for testing positive for recreational drugs earlier this season, according to multiple people familiar with the case.

Each player has failed at least three drug tests since he entered the league, according to one league source, including two test failures since the lockout ended in July. Williams already has accepted his suspension, according to another person familiar with the case, and Davis is expected to accept this week. Because their season-ending suspensions are part of a settlement, neither is expected to appeal, one person said.

Neither Williams nor Davis was made available to comment in the Redskins’ locker room following Sunday’s loss. The two left the stadium in street clothes and did not respond to questions from a reporter.

Spokesmen for the league and the union declined to comment Sunday, and Redskins Coach Mike Shanahan said he’d “received no information” about the suspensions. “But I will comment on it in the next day or two,” he said, “depending on what has happened.”

According to people familiar with the settlement, Davis, a fourth-year tight end, and Williams, a second-year offensive tackle, were part of a group of 11 players who failed tests for recreational drugs — believed to be marijuana — shortly after reporting for training camp in late July. The league and the union have been negotiating the fate of that group since August, mainly attempting to decide whether the NFL would grant those players a “grace period” because of the four-month lockout that halted league activities during the offseason.

Under terms of the settlement, nine of the 11 players will face no punishment for their failed tests during training camp. Davis and Williams, however, face suspensions because they later failed another drug test after the regular season began in September, according to those familiar with the deal.

Under terms of the league’s substance abuse program, a player with three failed tests for recreational drugs is usually subject to a year-long suspension from the NFL. Because one of the offenses came during the so-called grace period, the union negotiated the suspension down to four games, the typical punishment for a second offense.

NFL Commissioner Roger Goodell and DeMaurice Smith, the executive director of the NFL Players Association, worked personally on the settlement. The two sides agreed in principle to the deal Saturday. Sports Illustrated first reported the news Sunday afternoon.

Davis and Williams were aware this week that suspensions were likely and took the field Sunday afternoon against the New York Jets knowing they likely would be playing their final games of the season. Williams played the entire game at left tackle. Davis led the Redskins in receiving, with 99 yards on six catches.

One veteran player said teammates have been aware of the situation for weeks, but many Redskins players say they didn’t know enough about the pending suspensions to comment Sunday.

“Guys just got to be accountable,” linebacker Lorenzo Alexander said. “It’s a team. You have to know the rules, and whatever comes out, comes out. It’s a shame.”

Said cornerback DeAngelo Hall: “Obviously, we’re better with those guys. But we’ll have to figure out a way to play without them. The sun will rise. We’ll go play.”

News first surfaced of the failed drug tests shortly before Washington’s game at Miami three weeks ago. After that game, Davis said he had yet to hear from the NFL but had been briefed by his agent, Drew Rosenhaus. Williams said at the time, “I don’t know anything about that.”

Davis has career highs this season in catches (59) and yards (796). He is in the final year of his rookie contract and is scheduled to be a restricted free agent after this season. He was supposed to make $600,000 this year but will likely lose $141,176 by missing the final four games.

Williams, the fourth pick in the 2010 NFL draft, was set to earn $7.852 million in the second year of his rookie contract. He stands to lose nearly $1.85 million.

Williams had said as recently as Friday that he feels maturity has made him a better player in his second season. “This is a lifelong dream, so I just try to take advantage of every opportunity I get to play,” he said. “There are a lot of people who aren’t as fortunate to be doing what they love to do. . . . I try to lead by example, and that helps people when they see you going hard and taking nothing off of nobody.”

Williams and Davis would face a year-long suspension for another failed drug test, according to one league source.

Staff writers Mark Maske, Mike Jones and Barry Svrluga contributed to this report.