。
She worried that he might be in an accident.
Literal
She [topic-は] he [subject-が] accident [with-に] meet [is it not the case that-のではないか] [quotative-と] worried.
事故に遭う is a set phrase: 'meet with an accident.' The verb 遭う specifically marks encountering something unwelcome (different from neutral 会う). The whole proposition is wrapped in ~のではないか for the worry-pattern: 'might (he) be in an accident?'.