The phrase "stayed on" means to remain in a particular place or position for a certain period of time. There are several synonyms for this phrase, including "lived on," "resided on," "dwelled on," "occupied," "stuck around," "linger on," "persevered," "persisted," "remained," "continued," "abided," "endured," and "survived." Each of these synonyms has its unique meaning, but they all convey the idea of staying in one location or position for an extended period of time. Whether you use "stayed on" or any of its synonyms, the concept of remaining steadfast and persistent is key.