Hardy was initially convicted on misdemeanor charges of domestic violence against an ex-girlfriend last year, but after he requested a jury trial, the case was dismissed when his alleged victim, Nicole Holder, stopped cooperating with the district attorney's office.
The case was expunged from Hardy's record last week, but Deadspin recently released photos of an injured Holder, which created more controversy for the Cowboys. Hardy expressed regret via Twitter last Saturday for "what happened in [the] past."
Asked specifically if Hardy should be allowed to play, Staubach said in a telephone interview only that there should have been a more severe penalty.
Hardy was placed on the commissioner's list for the final 14 games last year, when Hardy was still with the Carolina Panthers, but he was still paid. The NFL initially suspended him for 10 games, but that was reduced to four games on appeal.
Staubach, who said in May that he wouldn't want Hardy as a teammate, said he hopes the defensive end is receiving help.
"I'm not aware of really what the situation is as far as him being in rehab or what he's doing to overcome his domestic violence, which is horrendous," Staubach said. "I have confidence that [Cowboys executive vice president Charlotte Anderson] knows that he's trying. I don't see that publicly in the paper or anywhere." Anderson, who is the daughter of Cowboys owner Jerry Jones, is on the NFL's conduct committee.
"I think he should've had a much stiffer fine and then he should be looked at every day to make sure he's doing what it takes so he doesn't ever commit another domestic violence act again," Staubach said. "... It's a sickness to me, whatever it is that makes you do that. For people to overcome that, hopefully he's doing what it takes. I don't know what's going on behind the scenes."
The Cowboys have said they expected criticism after signing Hardy in March, but coach Jason Garrett doesn't believe the scrutiny has been a distraction.
"I don't feel like it is at all," Garrett said Monday.
The Cowboys said they investigated Hardy's background all the way back to his high school days. They also talked to his college and pro coaches, and they were aware of what was said in police reports and court documents.
The team said it has laid out standards and expectations for Hardy that he has followed.
For Staubach, domestic violence is a little more personal. His daughter, Jennifer Staubach Gates, is a Dallas City Council member and the chair of the city's Domestic Violence Task Force.
Speaking last month on 1310 The Ticket in Dallas, Staubach Gates mentioned "mixed emotions," about Hardy being a Cowboy and said it would be "difficult to cheer for someone accused of what he's been accused of."
Staubach isn't sure the NFL or the NFL Players Association is doing enough.
"I think the NFL, there are some issues with the [NFLPA] where they should take a much more strict deal on this domestic violence and some of these issues in the NFL," Staubach said. "They're more sympathetic to the player than they should be at times.
"They have a responsibility to the player but also a responsibility to make this the best NFL for our fans. It's a combination of owners in the NFL and the PA and things just aren't hunky-dory between those two groups. The mission should be to create the best NFL -- and that's on and off the field."