"There's no guarantee he's ever going to play here," Gruden said. "He's got a lot of work to do -- personally, with the team, with the NFL, with himself -- before he even thinks about playing football again."
Gruden said it was a team decision to claim Foster, who was waived by the San Francisco 49ers on Monday following his arrest on suspicion of a misdemeanor domestic violence battery charge in Tampa, Florida, on Saturday night. The NFL placed Foster on the Reserve/Commissioner Exempt List on Tuesday -- a move that prevents the second-year linebacker from playing for the Redskins until the NFL's investigation into Foster's arrest is concluded.
The Redskins considered what the public reaction would be to claiming Foster before they pulled him off the waiver wire, Gruden said.
"A little bit. Yeah, I'm sure there was," Gruden said. "From [president] Bruce [Allen] and [owner] Dan [Snyder] and, obviously, [VP of Player Personnel] Doug [Williams]. But at the end of the day, we decided to make the move and we'll deal with the outcry, so to speak. But for the most part, this is a young athlete, a young person, who got himself into some trouble and we want to find out exactly what happened."
Gruden said his past experiences with Foster played a role in the team claiming him. Guden was impressed with Foster when he spoke with him before the 2017 NFL Draft.
"I spent a lot of time with [Alabama] coach [Nick] Saban and Reuben," Gruden said. "...They had a lot of players we spent a lot of time with, and [Foster] was one of them. And, at that time, he was one of my favorite players in the draft defensively, as a player, and one of my favorite interviews as a person.
"What's happened since then, I don't know really a lot about what's happened. I just have read a little bit about what's happened and it's not good. But we will get to the bottom of it by the end of the day. Like I said there's no guarantee he'll ever step foot on a football field here, but we would like to find out more about what happened."
Still, Foster's arrest on Saturday wasn't his first run-in with the law since being drafted 31st overall by the 49ers last year.
Foster was charged in January in Alabama with second-degree marijuana possession. That charge was eventually dismissed after he completed a first-time offender diversion course, but he was suspended the first two games of the season for violating the NFL's conduct and substance-abuse policies.
Foster faced more serious charges for an incident in California in February. He was initially charged in April with felonies for domestic violence, making criminal threats and weapons possession after being accused of beating up his ex-girlfriend. A judge ruled there was no probable cause on the first two charges after the ex-girlfriend recanted the allegations.
In Saturday's incident, the alleged victim told police that during a verbal altercation with Foster, he slapped her phone out of her hand, pushed her in the chest area and slapped her with an open hand on the right side of her face. Officers observed a one-inch scratch on her left collarbone, according to police.
When asked by a reporter why the Redskins decided to claim Foster off waivers rather than wait and see how his legal and potential disciplinary issues play out, Gruden responded: "That's a good question, we [probably] could have done that. But we claimed him and we chose for him to be part of our organization."
Gruden also wouldn't say whether he believes, at this point, Foster deserves a second chance.
"I think a lot depends on it," he said. "And we don't know if he's going to get a second chance, quite frankly. We don't know. There has to be a lot of recovery, he's got to go through the process with the league, with the police. Individually he's going to have to get some help, in counseling.
"We understand that it's going to be a long process for him. But he's a young player. He made a mistake or two and at the end of the day we decided to take a chance and deal with it."
The Associated Press contributed to this report.