The power brake booster is only there to assist with braking action when the engine is running and you are getting vacuum to the booster. When the engine is not running there is no assist from the booster, the brake master cylinder will work the same as a vehicle with non-power brakes.
The brake master cylinder creates the pressure for the brake system. The power booster only assists in applying pressure to the brake master cylinder.
If you are having to pump the brake pedal to create pressure ("a stiff pedal") you have other problems with your brakes ("gremlins").
You need to make sure your brakes are bled properly at the wheel cylinders and the master cylinder. If after bleeding you still have soft pedal problems, you may have internal problems with the brake master cylinder and it may need rebuilding or replacing.
If you haven't done so, you should also pull your wheels and check the brake components. Ensure you wheel cylinders/calipers are not leaking, the brake shoes/pads are in good condition, and the springs, adjusters, and other components are in good shape.