Owner and general manager Jerry Jones is not worried about Elliott being away from the team during the suspension.
"I think he's got a good plan, and I know he's going to be doing stuff," Jones said after the Cowboys' 27-7 loss to the Atlanta Falcons on Sunday. "He's going to get away, and he's doing some things that will help his career and his life, and so, no, I'm not as concerned about that."
Elliott cannot have contact with the front office and coaches during his suspension. He can have contact with the team's athletic training staff.
Jones would not get into where Elliott will be during the suspension. Reports had Elliott spending time out of the country.
Dak Prescott said he has communicated with Elliott since the suspension kicked in.
"He's doing well," Prescott said. "We just shared text messages as friends -- not as employees or teammates, not even talking about football for the most part."
Elliott was able to play in the first eight games through a number of legal decisions, but he lost a temporary administrative stay that kept him on the field in last week's win over the Kansas City Chiefs. He will miss at least the next four games, pending a Dec. 1 hearing, and he is likely to miss the next six.
The Cowboys missed Elliott, as the team rushed for 107 yards on 21 carries. Alfred Morris led the Cowboys with 53 yards on 11 carries but had just 8 yards on six first-half carries. Elliott had 783 rushing yards in the first eight games of the season, with four straight games of more than 90 yards on the ground.
Jones has supported Elliott throughout the travails of a domestic violence charge that first came to light in July 2016. Although Columbus, Ohio, authorities did not charge Elliott, the NFL said it had persuasive evidence that he committed domestic violence against a former girlfriend and suspended him six games under the personal conduct policy.
Jones has said numerous times that the NFL has not treated Elliott fairly.
Asked if Elliott learned anything through the process, Jones said, "I think all of us continue to learn, and at his age, he's learning things every day," Jones said. "So there's no question what I want for Zeke is that he's a better person, not only for whatever he's doing over these next six weeks, but hope he's a better person for the kind of year he's having, the kind of year he had last year, and he'll continue to be a better person."
A backdrop to the Elliott case was Jones' removal from the Compensation Committee by Atlanta owner Arthur Blank last week after Jones threatened a lawsuit against the NFL and several owners for the impending extension for Roger Goodell.
Jones and Blank did not speak before the game.
"I've had games where I didn't visit [with the opposing owner before a game] for whatever the reasons," Jones said, "but it's rare."