Even if June 1st isn't what it once was, there are still good players available in free agency:
Kendyl Jacox is a big center/guard who has started 85 games in his career...
Keith Newman, Tommy Polley and Chris Claiborne are all linebackers with the kind of size Parcells likes, all of whom have started over 60 games in the league... they're all also in the 4.55-4.65 second 40 range...
Lance Schulters and Antuan Edwards are talented, experienced safeties... Ifeanyi Ohalete would be a nice addition at safety if all you're looking for is quality depth, he can play both free and strong safety...
Terdell Sands is a massive nose tackle, but strictly a backup... that's OK, the Cowboys have Jason Ferguson, what they need is a backup...
Jacox, Newman, Polley, Claiborne, Schulters and Edwards would be fairly pricey, but the Boys have cap room to sign one or two of them... Ohalete and Sands would be much more reasonably priced...
All of these players would shore up parts of the roster that could still stand a little shoring up...
There are other, lesser players out there too-- Rocky Calmus, Nick Rogers and Barry Gardner at linebacker... Kevin Johnson, Troy Edwards and Dez White at wide receiver... Nick Luchey, Jonathan Wells and Paul Smith at fullback...
If the Boys are still in the mood to spend a little money after the draft, there are options out there that could improve the team... but let's remember, they're gonna want to earmark some of their remaining cap room to try to sign Witten, Newman and Roy to contract extensions... perhaps not all 3, but at least 2 of them, I think...
Though the Boys are reportedly some 12 million under the cap, you've gotta factor in the money to sign their draft picks, fund a practice squad... add in the money they might need to re-sign some of their own young veterans, and there's probably not much more than 2 to 3 million left for pursuing free agents... then again, there are contract renegotiations they could work to free up more cap room, if they really, really wanted to pursue some more veteran free agents...