Jason from Over the Cap did a tremendous job explaining the details of the "June 1st" date in the NFL as it relates to the salary cap and signing players. The Browns can't really take advantage of any of the tricks mentioned, but that's a good thing, because it means your front office(s) have already been doing a solid job managing the cap. The rules are typically meant to help teams who don't even have enough cap space to sign their draft picks, but that's not a problem for Cleveland:
The Browns have the second-most cap space in the NFL, only behind the Jacksonville Jaguars. Even after they sign all of their draft picks, Cleveland will still have the second- or third-most cap space in the league. Nonetheless, let's take a brief look at what the Browns technically could have done in relation to the June 1st date:
Post-June 1st cuts have their guaranteed money spread over two seasons. Let's take DE Desmond Bryant as an example; his contract is simple to describe because his base salary from 2014-2017 is not guaranteed. Currently, in each year from 2014-2017, Bryant's signing bonus cap charge is $1 million (pro-rated amount of his $5 million signing bonus, split over a five-year contract).
If the Browns had cut Bryant on May 25th (or any date prior to June 2nd), the Browns would have carried $4 million in dead money against the cap in 2014 for Bryant. Bryant would not have counted against the cap in 2015-2017.
If the Browns cut Bryant on June 3rd, he would count toward $1 million against the cap in 2014, and $3 million against the cap in 2015. Again, since the Browns have so much cap space, this rule would actually hurt the Browns. If Cleveland only had $500,000 in cap space, though, you can see how the $3 million in savings (pushed into 2015) can offer temporary relief to sign your draft class.
The Cowboys are actually going through this with Miles Austin. They cut him back in March, but with the "post-June 1st designation." Releasing Austin saved the Cowboys $5.5 million against the cap, but they haven't been able to use the credit on those savings until after June 1. It hurts their 2015 cap, though, because that $5.5 million shifts to the 2015 cap for Dallas. None of what Dallas did effects what is going on with Austin in Cleveland.
- Signing players for compensatory picks. Players signed on June 1st or later do not count against a team's compensatory pick formula for the following year's draft. That means for any veterans who are still out there, you might start seeing them get picked up. This is not advantageous to Cleveland, because they signed a lot more free agents than they lost this offseason, so they won't be getting any compensatory picks in 2015. However, if Cleveland hadn't signed a player like WR Miles Austin when they did, another team might have struck after May 31st.