2006 Chevy Silverado 5.3

I also can drive my truck for a short period, but after a while I don't even have to step on the breaks. The truck just stops on its own.

I think your master cylinder is bad. I have had this issue before or maybe a proportioning valve.

But if the master cylinder is bad, I wouldn't get any fluid going to the caliper.... correct???

No it can still free flow and in this failure it is not releasing pressure. Back off on the bleeder valve when its stopping itself and see if its squirts and relieves the pressure, do both sides, brakes should be free until you drive and hit the brakes it will start all over again. Its happened this way to me before. I never heard of it from anyone else either. But like I said I could relieve the pressure and it would do it again. The further I tried to drive the tighter the front brakes became until it stopped all movement.

Master cylinder was checked it's good, booster it's also good, put in a new booster vent. Replaced brake lines and the problem is still happening?????? New calipers, rotors, brake pads,hoses & brake lines... Only thing we have not done is taken off all the new parts to check to see if possibly the driver side caliper could be bad.

I am gona double down unless you have incorrectly installed those replaced parts its the master or proportioning valve. If Brakes pads are tightening down without your foot on the brake pedal.

Otherwise its some other issue all together.