Thanks everyone for the input. Got some testing to do, will let you know what happens.

:)

UPDATE:
Using the Chilton manual suggested tests, I ran the tests for the Power Brake Booster and check valve, they passed.
However, just because I could get the parts right away I went ahead and changed the Power Brake Booster check valve AND I also changed the Power Brake Filter Canister which is between the Check Valve and the carb ( A feature on the C3's 78 and above).

Didn't change the situation, car still stalls approaching a stop. There was a minor change in that instead of completely stalling out while not in motion, when I step on the brake --- it intermittently stalls and sometimes catches itself and returns to idle. (doesn't matter if I'm in park, neutral, reverse or drive - happens in all cases). Before it would just stall out. I check the hoses and connections all the way to the carb and everything appears solid and tight.

Did you check the check valve before installing and also verify it's in the correct direction?

Does your car have an idle stop solenoid?

|UPDATED|7/11/2015 5:22:26 PM (AZT)|/UPDATED|

Yes I did check it (the old one was good too) and it's installed correctly, actually there's only one way because on end is bigger than the other, plus I also replaced the rubber seal on the Booster it goes into and made sure it was seated properly.

I believe I do have a Idle stop solenoid, it's right off the linkage on the driver side of the carb. Also I have AC and AT. But I thought those were on the L82 engine, I have a L48 (350/190hp).

Here's a wildshot....does your automatic trans have wires running to it? Had the same problem happen with an old car of mine, not a Corvette but Cavelier. When I would come to a stop the converter would not unlock and engine would stall. If there are wires going to it pull the plug and see if it still stalls...never know. I pulled plug and it did not stall, just didn't have overdrive.

danascar - that's not that much of a long shot. The mechanic that had the car checked a number of connections including some involving the transmission. Everything seemed in order per him.

The '78 cars dint have the lock-up trans originally. I already considered that, and that's why I asked if it felt like something was dragging/lugging the engine down at a stop. A stuck lock-up is similar to trying to stop a standard transmission car without pushing the clutch pedal down.
A non-lock up 350(which is what the car should have) will have no electrical connections on it anywhere. The lock-up 350 will have a connector on the driver side of the trans, just behind the shifter shaft. IF the car has a lock-up style trans, even without any electrical connection, the lock-up could be applying due to a stuck valve, or a hydraulic leak in the circuit. Even so, this would lug the engine at stops, not shut it down instantly.
The mystery continues....

Ok gang: here's what the issue was....believe it or not.
I believe (without reading previous postings) I stated that every time I stopped the car, the engine would stall out. There was certain occasions it wouldn't but they were few and far between.
I had the car towed to Corvette Masters in Maitland, Fl (Orlando). In 15 mins they found the issue!
The ignition wires, under the dash, had dropped down and the brake lever, when I stepped on the full brake, would tug the wires from the ignition and thus shut the car off!! How simple!! If I gently touched the brakes it might not happen, but almost always it would.

If you live near the Orlando area I highly recommend these guys, I spent some time talking with them and they really know their stuff.

Thanks to all of you for taking the time to respond and your suggestions, it 's great to know the community is always here to help!

Next up for me, is taking the steering column apart to put a new lower horn assembly in there......

Milt

Joel was on the right track!  

Glad you found it.  Surprised that the wire would reconnect when the brakes were released.  Sounds like it was pulling on a terminal and breaking contact and restoring contact when the tension on the wire was released.