She wrote to tell me that our friends died in a strange accident that involved a vacuum cleaner.

involved 是动词 involve 的过去分词形式。involve 的意思是"涉及、包含、牵涉"，表示某事物与另一事物有联系或参与其中。在这里 involved 表示"被卷入、被涉及"的意思，说明吸尘器与这起事故有关。