If he PUPS can't they keep him there right up until the start of the season?
As long as he is on PUP at the start of camp (or whatever the failed physical designation is at that time) he can stay on PUP and be eligible to come back after Week 6 with a 3 week window to practice before having to choose to put him on the active roster.
Bud Adams told me the franchise he admired the most was the Kansas City Chiefs. Then he asked for more hookers and blow.