But you are right someone will arbitrage the price, like scalpers selling concert tickets.
A well-known anticompetitive tactic is for a big player with a vast bank account to move into an area and eat losses while waiting for their competitors to starve. Well observed in the 90's movie rental market, so certainly real.
To successfully perform dumping, you have to have access to excess supply capable of disrupting that market.
So if that's the expected outcome, it might be better to prevent competitors from building factories in the first place.
(Legitimately asking: I don't know the answer ... but based on most US business law my strong suspicion is ... no, they don't.)