Your worry is widely believed by many, but it is an apparition. From Tom Woods’s book Rollback:
This widely believed scenario is actually a phantom. Economist George Stigler declared that ‘today it would be embarrassing to encounter this argument in professional discourse.’ For one thing, the firm attempting it loses disproportionately, for it must take losses on its large market share. Consumers, meanwhile, stock up on items at these fire-sale prices, making it all the longer before the firm can expect to make up those losses. If the firm does manage to drive everyone else out of the business, its problems are only beginning. Any one of these firms can start up again at any time as soon as the ‘predatory’ firm begins charging the high prices it has been craving. If those firms literally went bankrupt as a result of the predatory pricing scheme of their competitor, then other entrepreneurs would have been able to acquire their assets for low prices at auction, making these firms much fiercer competitors as a result.
He goes on to say that scholars actually have a hard time finding an example of predatory pricing, where firms lower their prices to the point where their competitors go out of business, then raise their prices.
malo periculosam libertatem quam quietum servitium
I am an aristocrat. I love liberty; I hate equality. - John Randolph of Roanoke