The Cards signed outside linebacker Isaiah Irving off the Denver Broncos' practice squad on Thursday. The Cardinals cleared a roster spot by placing Jones on injured reserve.
The exact plan for defensive coordinator Vance Joseph to fill Jones' on-field role remains a work in progress.
"We'll always have four guys dressed for the game, so whoever plays what snaps ... we're still working through those parts of the game," Joseph said. "We got DK (Devon Kennard) back at practice, and obviously he's a big part with Chan being out so we'll see how he progresses.
"Nothing should change as far as the base and sub(-package) concerns. If DK is full-speed, he'll play full time along with Haason (Reddick) and (Dennis) Gardeck is backing both spots up."
Joseph said Reddick in particular had a good practice Thursday.
"I see a guy who is very comfortable in his role," Joseph said.
Irving spent the last three seasons with the Bears, after arriving as a undrafted free agent in 2017. The 6-foot-3, 254-pounder has a sack and a fumble recovery in 33 career games, all as a reserve. But coming in this late in the week, the Cardinals will have to see if he'd be able to play a role on such short notice.
The loss of Jones is a harsh blow to the defense. Kennard should return this week after missing two games with a calf injury. Kylie Fitts has been in the rotation, but he has missed practice both Wednesday and Thursday with a hamstring issue. Gardeck also was missing both days with a foot injury, although Gardeck said Thursday he was confident he will play against the Cowboys Monday.
The Cardinals also still have undrafted rookie Reggie Walker on the practice squad.
Joseph added that defensive lineman Zach Allen has the versatility to play outside linebacker/edge rusher in certain situations, a role Allen was already taking part in against the Jets after Jones went out.
"Zach as a college player was a defensive end in a 4-3 front, so our first-, second-, third-down stuff, Zach is capable of playing defensive end," Joseph said.