Here's a good one. My 78 C3 with standard 350 now stalls out when coming to a stop (stop signs, traffic lights, any kind of reduction in speed). It runs terrific otherwise (on the road and idling). This recently started, shortly have having Hooker headers and straight pipes installed - it did run ok for a few days. Only occasionally does it seems to "catch" and not stall. but very rarely. Ok I know you're thinking well we now have a new air ratio to deal with as the exhaust is exiting much freer than before. My mechanic thought the same thing, at first. He adjust the carb several times, thought it he had it, but it stall out almost immediately after I picked it up. So he's gone over all the vacuum pressures, all the grounds (because he started thinking it might be an electrical problem). However, nothing has corrected the situation. He's been working on it a couple hours a day for the last week plus. The problem is you can't create the problem in the shop.He's down to possibly the ignition switch (which might be possible - I have a no horn and have traced the problem to steering column as I'm sure a wire is busted in there. I've also had to replace the light switch among other aged parts! (maybe I can get the car on medicare! LOL). Any thoughts anyone run into this before?

Does it just suddenly shut off, does it run rough and die, or does it feel like something is dragging the engine down until it dies?
Does it fire right back up?
Does it idle well in park/neutral?
I've never seen or heard of installing headers changing the air/fuel mixture enough to cause any problems, especially causing the engine to die.
My first thought is wiring damage for either the install, or heat from the headers. If it was an ignition switch, you would have had the same problem before the exhaust install.
Need more info...

Also is it an automatic or a stick?

Apple: Thanks for the response, since I got it back from the mechanic I drove it for awhile testing it to see under what circumstances the failure occurs.  Let me answer your questions first.....
It's an automatic
It just dies straight away (as I said earlier it catches itself on a rare occasion and continues to run).
It starts right back up
it idles fine in park, neutral, and Drive (this last one is important) even with my foot on the brake.
Maybe I wasn't fully clear on the headers, they are Hookers and go to a 4" straight pipe on the sides of the car, I have glass pack mufflers installed there (no cat converter). The original muffler system is gone.

Anyway here's what I found almost anytime i put the brake pedal down fast everything just dies, the engine dies and all the gauges go dead, including the amp gauge (remember the ignition is still on). Now I can restart the car, put my foot on the brake and nothing happens in neutral or park and I can put the car in Drive and it's fine to move forward. Driving along at say 35 mph and can quickly pump the brake pedal and make the car almost stall out at will. WEIRD.

I can coast up to a stop sign by using my right foot to rev the engine and my left foot to gently use the brake pedal and the car keeps running. I normally am a one foot (right) driver.

This certainly appears to be an electrical issue of some sort. Either in the harness or the ignition system. I know that a bad brake pedal switch can foul up the turn signals I'm wondering if it can have any other effect....I need to go through the Schematic Electrical book I have for the car.

This is what we needed. I would be checking the brake booster, and the vacuum line/check valve for the booster. When you hit the brake hard like that, it dumps the vacuum out, and it's like having a HUGE vacuum leak on the engine all of a sudden, so it dies.
The gauges doing what they are doing is most likely a result of the engine dying.

Supposedly the mechanic has checked the vacuum though out the car, but hey who knows.

I'm going to start with the assumption that the booster itself is ok, since there is no change in the cars braking characteristics.

So how do I know if the check valve is bad without buying a new one?

Also I'm not sure I fully agree with you on the gauges, but that's not important.

Thanks for you help!

Just going on the assumption that the car was NOT doing this before the exhaust work.

It's entirely possible that the brake pedal/linkage is rubbing on the harness under the dash, OR the firewall is flexing enough to cause the fuse panel/firewall pass-thru to loose contact. Do you know if the headlights would also go out when this happens, or could you try to see if they do? Another possibility is that in the process of installing the headers, the wiring on the starter was moved enough to finish off a loose connection for one of the fuse links. Can't say why popping the brakes would excite a loose connection there, but....gotta think out of the box sometimes.   You could check for this by hooking a multimeter, or test light up to the large red wire on the alternator. Should have 12v there all the time, unless there is a problem with the fuse link/wiring from the starter. If you loose voltage there when the car dies, you've located the source of the issue. That same 12v circuit also powers the ignition switch, and just about everything on the inside of the car.....

What happens when you stab the brake pedal while the car is running in park? I agree with Dr Joel, It does sound like vac and booster related.

just a thought   when installing headers on older car,tight spot   things get moved I think you have more than 1 problem,start at easest ,something gets knocked off buy power booster  it happens,get buy starter wiring this a good spot to look,wire got moved  sure. sometimes you think of things and say that can,t be problem but the easy one are aways skipped because it must be A big problem,many years in car busness  people look for problem that may been there already now your looking for problem,stop ,think what looks out of sorts  the easy ones are always the hardees.stop think you will find causes    take your time,i seen more problems from headers being put on stock cars,something always gets moved.dwa

I suspect you are not pushing the brake as hard sitting as when stopping.. all the vacuum may be okay under the hood and work with a given level of brake pressure, but leak severely under harder brake pedal pressure application. I suspect Joel may be on the right track, but try this. Idling in gear push the brake very hard and fast. See if the engine reacts. If it does disconnect the vacuum line to the brake booster and plug this side going to the engine. Hit the brake hard again. If the engine reacted with the line connected but not with it plugged the booster or check valve is the problem. If so, you will find the check valve where the vacuum line connects to the booster. Remove it and blow through it. If you can blow both ways that's the problem. If you can only blow through one way the booster is the problem. If none of this has an effect, flow Joel's lead.