Dividends are paid from company earnings (profits), not stock, and as such, stock price doesn't affect the ability of the firm to pay dividends. They could both have the same underlying cause though - which is, a deteriorating business condition that reduces earnings. Otherwise, e.g. if Coke's stock price falls by 50% in a recession, doesn't mean it will cut its dividend.
Stock prices come from the same forces that shape dividends. There's a reason that dividends from diverse companies all tend to cluster around the same percentage of the share price.
