Jones told reporters Friday night that the door has been closed for the possibility of Hardy's return.
"Yes," Jones said when asked if Hardy being a Cowboy in 2016 was off the table.
The Cowboys made it official not to re-sign Hardy only a year after he was released by the Carolina Panthers due to his troubles with the law off the field.
The Cowboys signed Hardy to a one-year, $11.3 million deal in 2015. He recorded six sacks, 35 tackles, an interception and a forced fumble in 12 games after serving a four-game suspension by the NFL.
Cowboys fans, former greats of the team and state and local politicians spoke out against Hardy after he signed with Dallas because of a high-profile domestic violence incident in North Carolina. Hardy spent most of the 2014 season on the commissioner's exempt list before charges were formally dropped.
Photos showing bruises and abrasions on the body of Hardy's former girlfriend were published by Deadspin last year. The Cowboys claim they did not see the pictures before signing Hardy even though the NFL acknowledged seeing the graphic evidence during its own investigation.
Hardy, who was convicted on domestic violence charges in a bench trial before the charges were dismissed following an appeal, said in the ESPN interview earlier this month, "I've never put my hand on ANY women. In my whole entire life. No sir. That's just not how we're raised. As you can tell, like I said again, it's the Bible belt. It's just something that's, I wouldn't even say frowned upon, just something that's nonexistent in most southern homes."
Interviewer Adam Schefter then presented Hardy with photographs of the accuser's injuries.
"I will stop you right there and say that I didn't say that I didn't do anything wrong," Hardy said. "That situation occurred and that situation was handled but ... saying that I did nothing wrong is a stretch but saying I am innocent is correct. Yes sir."