McClain and Leary had their physicals on Monday, but coach Jason Garrett said neither would take part in team drills and will work mainly off to the side during the three days of practice to avoid the risk of injury since they were not part of the offseason program.
McClain attended the early part of the offseason program but has spent most of his time in his native Alabama tending to what Jason Garrett called family business. Leary has been seeking a trade since before the NFL draft in April.
The Cowboys signed McClain to a one-year deal worth as much as $5 million, including a $750,000 signing bonus. He missed most of last year's offseason program, choosing to rehab a surgically repaired knee in Alabama, but reported to the minicamp.
Leary signed the $2.553 million contract the Cowboys tendered him as a restricted free agent in March before the draft in hopes of facilitating a trade. The Cowboys had several discussions with teams during the draft but were not offered enough to part with Leary. Leary started every game he played in 2013 and '14 and opened last season as the starter at left guard before he was replaced by La'el Collins.
Last week Garrett said he had spoken to both players but was not sure whether either would attend the minicamp. Had they skipped the minicamp, they would have faced fines of $12,675, $25,525 and $38,290 for each day they missed.
After Thursday, the players are off until the team flies to Oxnard, California, for training camp on July 28.