Where would my Scottrade money go in a GREAT DEPRESSION?

Someone else asked a very similar question with no good specific answers. Yes I know that investing in stocks at any time is risky. What I mean is...Say I invest in a good company. Say its Guarantee Wonder Widget CO. GWWWCO. I go to Scottrade and type in the code and click on buy. Now I have 100 shares. Suddenly the stock market takes a "VERY" bad fall. It goes down, down, down, and doesn't come back up (Like the Great Depression- or worse) Meanwhile Wonder Widgets are selling like hotcakes. GWWWCO is doing great. Can I take a horse and buggy to my local Scottrade office, wait in line next to the people begging for bread and get my $$$.

The reason I ask. I just opened a Scottrade account. Some of the terms and conditions sound like they might have potential- not in my favor. The first registration page gives specific info about marginal investing. I'm not doing that. I don't think? (not yet) It also mentioned having the right to sell my stock. I know that during the Great Depression alot of folks were forced to sell their stock wether they wanted to or not. Is that only because they owned marginal accounts? I figure Scottrade is another company like any other. Its backed by some big insurance company similar to the FDIC. What if Scottrade folds? Where do my shares go?

I'm not sure I understand your question. Are you asking if you can withdraw money from your local scottrade office? Sure, but I think they have to mail a check to the address they have on record. At least that's the way it used to be. Are you asking if you can get your money back after an investment goes down, then the answer is no, you can only take out what the investment is worth, and if its worthless you're out of luck. If you're asking where the value goes when that happens, it essentially evaporates. When you buy a stock, you are transfering your money to the seller of the stock on the assumption that you will be able to get somebody else to transfer more money to you later. If that assumption doesn't turn out to be accurate then you lose. If you're asking if it's possible for one company and its stock to do well when the market as a whole goes bad, then yes, absolutely.
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Updated after your update:

As you have guessed, the only way a brokerage firm can force you to sell your shares is if you have a margin account. And that's because in a margin account you have borrowed money from the brokerage to buy those shares and the brokerage wants its money back. You generally have the option to give them money or sell stock, but in the event of a really fast market, the brokerage can sell you out to get their money back.

Also, as you have guessed, the brokerages carry a ton of insurance. Scottrade is safe. They aren't going to go bankrupt and disappear with your stock.

If you invest in individual companies, your investment is only affected by those individual companies, not the overall market.
So let's say in the unlikely event that the stock market crashes, but your stock is one of the very few that is doing well. Your money will still be there and worth the share price times the number of shares you own.

You don't have to wait in line anymore.

We now have Visa Debit Cards.

All you have to do is sell your GWWWCO Shares and wire the money to your bank account.