My 2007 6.0 has no power brakes at all when the motor isn't running. The power brake unit has what looks like an accumulator that would give some assistance at first when the motor is shut down.

I was pulling my 5th wheel plus my utility trailer (about 12,500 total trailer weight) and a bearing in a fan belt idler fell apart and spit the belt off. It took forever to stop with a lot of pedal pressure. Afterwards I did realize that I should have applied the trailer brakes manually to help. Today I was hitched to my 5th wheel (about 9,000#) and I put the truck in neutral and applied the brakes and stopped. I shut the motor off to turn the engine controller to a lower setting and I immediately lost power brakes and I had to push very firmly to hold the rig stopped on a very slight grade. Vacuum boosters have enough reserve for a couple of stops, don't hydraulic units have this? How do your trucks act?

 

I have a friend that has an early 03 with a 7.3L and I checked his. He had boosted brakes with the motor off for a couple of applications. I replaced mine with a Delco rebuilt unit from Rock Auto and now I have some boost for a couple of applications with the engine off, but it's not quite as good as I think it should be. One surprise was that now the brakes and the power steering take noticeably less force to operate so I guess my old booster was bypassing some. Also I had a hard stop and after wards the brake pedal felt firmer like some air in the booster bled out. With the old booster the brakes seemed a bit weak and you had to push harder than you should have to. Now it's way better.

 

Thanks for the update..