The death of Supreme Court Justice Antonin Scalia has cast a cloud over the outcome of class-action lawsuits that target businesses, leading Dow Chemical Co. to pay $835 million to settle a case rather than risk an appeal without the conservative justice.

Dow Chemical’s decision is a signal of worry among businesses with cases before the high court, which could operate without its former 5-4 conservative majority well into next year. Justice Scalia was an ally to companies in their decadeslong push to block multiparty lawsuits...