When the New York Giants waived/failed physical tight end Jake Ballard on Monday, they did so with the likely intention of placing him on the Reserve/Physically Unable Perform list as soon as he claimed waivers, which would have moved Ballard off their 90-man roster.
The Patriots put a wrench to those plans on Tuesday, claiming Ballard off waivers. He now is on the team's active roster, and counts against the 90-man limit.
Going forward, the most likely option for the Patriots appears to be to keep Ballard on their active roster, placing him on the Active/PUP list at the start of training camp. At the final roster cut-down to 53 players, Ballard would then be placed on Reserve/PUP, keeping him out for at least the first six weeks of the season, and allowing him to return to the active roster as late as Week 13.
If the Patriots want to clear Ballard off their 90-man roster prior to roster cut-downs, he would have to first be either waived/injured or waived/failed physical, which would expose him to waivers and a likely re-claim by the Giants.