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That's not how dividends work. Dividends are related to how much profit/cash the company has, and how many shares are outstanding. The price of an individual share doesn't effect that, only issuance of new shares and changes in cash flow.

Shares frequently crash in conjunction with economic pullbacks, which mean lower revenue/earnings for companies, which means less spending by those companies, which means lower revenue/earnings for other companies, and layoffs, which means lower earnings for workers, which means less spending, etc etc.

Shares of individual companies also frequently crash for reasons totally unrelated to economic pullbacks, and thus none of those things are guaranteed to happen simply because a share now costs less.

Sure, but I assume we're generally talking about index/portfolio investing here when we talk about stocks in general?

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