What happened to investors during the Great Depression who managed to hold onto their assets? Were they fine a few years down the line if the companies they invested in didn't collapse? Are there noable examples?

It depends on when and how they bought. If you got some stocks in 1920, paying out of your hard-earned wages, you were fine; July 1920 is a convenient starting point because the Dow Jones is at about 1000 then. It goes down to about 750 at the nadir of the crash, but recovers the 1000 level by 1933 and from there it's all upwards; when you consider that the stocks would have been paying dividends the whole time, someone who bought in 1920 would come out fine.

On the other hand, if you bought at the height of the boom in 1929, say the day before the crash, ouch. Double ouch if you bought on margin; in case you don't know how that works, you put up 10% of the price of the stock, and the broker lends you the rest with the stock as collateral. If the stock price rises, you can sell the stock, pay back the loan, and pocket the price rise. If the stock price declines, you have to either put in more money so that your equity remains above some level (today 25% minimum, but the law that established that minimum was written after the Great Depression, by one of those odd coincidences), or give the broker the stock - so you lose your whole investment. Still worse, imagine this scenario: You buy some stock priced at 100 dollars, putting in $10 of your own money and borrowing $90 from the broker. The stock declines to $50; your equity plus collateral is now $60, your loan is $90, so the broker calls you up to say "either put in 30 bucks, or give me the stock". You think the market will rise again, so you put in the $30. The stock declines to $25; you're on the hook for another 25, which you put in. The stock declines to $10, which is what you originally paid; you don't have the fifteen dollars you need to cover the margin, so the broker repossesses the stock, probably cursing himself for lending to such a deadbeat. Your loss is the whole $65 you put in, and you don't even have the stock any more.

The invention of margin buying, and its becoming a widespread tool, was one reason for the stock market boom in the twenties; it follows that a lot of people were buying on margin, and it is likely that most of them were wiped out right away in the days following the crash.

If, however, you either didn't buy on margin, or you had sufficient cash reserves to cover your calls, you were still not in great shape if you happened to buy just before the crash. The Dow peaked at 5200; it didn't recover that level until 1959! That's some long-term investing, there. However, the comparison is a bit misleading in three ways: First, the Dow is not the stock market as a whole - it's just a convenient measure because it goes back so far and is easy to find data on. If you invested in Random Non-Dow Company Inc, you might do better or worse. Second, that 1959 level suffers from some inflation; without doing the math, 1963 when it hits 6000 might be a better estimate of recovery in real terms. Third, the index value doesn't account for dividends. If you reinvested dividends, especially during the crash itself so that you got a bunch of cheap stuff and benefitted from the subsequent recovery, you would get your money back way more quickly - not giving a specific year here because it's so dependent on the yield.

TLDR: If you bought in 1925 and reinvested dividends through the crash, you were probably fine. The closer to the crash you bought, and the more you bought on margin (or sold in a panic) the worse off you were.