、。
She shed a flood of tears when her beloved dog died in an accident.
Literal
She [topic-は] doted-on [attributive] dog [subject-が] accident [from-で] died time, lots-of [of-の] tears [object-を] shed.
A nicely complex sentence with several pieces. かわいがっていた is a relative clause modifying 犬 — かわいがる means 'dote on, treat with affection' (literally 'consider cute'); the past continuous form expresses ongoing affection up to the moment of death. 事故で死ぬ ('die in an accident') uses で as the cause/circumstance marker. The whole clause かわいがっていた犬が事故で死んだ時 ('at the time when the dog she had doted on died in an accident') is itself a temporal subordinate clause with 時 ('time'). 涙を流す ('shed tears') is the standard idiom for crying — literally 'flow tears,' more vivid than just 泣く ('cry').