The chart below highlights two issues:
1) How long did it take for a stock to get to breakeven?
In the case of Union Carbide, the stock nearly recovered all of its losses by 1937 before the next major stock market decline. The loss of nearly -90% was difficult for anyone to experience so it is assumed that most investors would have sold the stock at or near the depths of the decline in 1932.
2) What happened to the dividend during the stock market crash and "Great" Depression?
The dividend tracked earnings with a lag of 9 to 12 months. As earnings bottomed in 1932, so too did the dividend. However, in spite of being in a "Great" Depression, earnings steadily grew for Union Carbide until the 1937 peak. This increase in earnings was reflected in the growth of the dividend.