The relevant date is the ex-dividend date. You are only eligible to receive the dividend if you hold the share on that date, thus the value of the share is decreased by the dividend amount immediately afterwards. The risk exposure regarding the exact dividend amount is very concentrated on the ex-dividend date and not spread out. Indeed, it was or is common for some institutional investors to lend out their shares around the ex-dividend date, though mostly for tax reasons.
If the company is stable and boring and not growth-oriented, the dividend will typically be the company's earnings per share across the previous quarter or year. However, this is not an inherent property of dividends. The company can freely decide on the dividend amount, which could realistically be anything between zero and almost the current share price. It is not unheard of that companies take on debt and/or accept negative growth in order to have enough cash to pay a stable dividend.
If the dividend is based on prior earnings, then there is a kind of averaging effect because the company earns this money across multiple months. But the same is the case for case for companies that don't pay dividends: their earnings increase the value of the company and therefore the value of the shares as well, and this growth is also spread out across multiple months.
You propose a scenario that a sudden dip would force you to sell all your shares in order to get the same amount of money as a dividend. But if a company were to pay out all of its value as a dividend, the company would be worthless afterwards – the end result is the same. While it's intuitive that a company's share price cannot fall below the dividend, it's more accurate to say that the share price cannot reasonably fall below the book value of the company's assets. Also, the dividend is not known in advance.
Caveat: this answer assumes an efficient market that is able to price assets correctly, that bookkeeping is correct and non-fraudulent, and that the company is not close to bankruptcy.