The people who came the next day encountered danger.
Literal
Next-day come-[attributive-た] people [topic-は] danger [to-に] encountered.
見舞う ('to visit [someone sick] / to befall / to strike') is a verb with two main senses: visiting a sick person, or being struck by misfortune. Here it's the misfortune sense in passive form 見舞われる — 'being befallen by.' 危険にみまわれる = 'struck by danger.'