From Longman Dictionary of Contemporary Englishstay on phrasal verbCONTINUE/NOT STOPSTAY/NOT LEAVEto continue to do a job or to study after the usual or expected time for leaving He resigned as chairman, but stayed on as an instructor. → stay→ See Verb table
Examples from the Corpus
stay on• Alvin came here initially as a session musician, but he stayed on.• There was little encouragement for those over 65 to stay on after retirement.• About 40 members of the audience stayed on after the performance for a glass of wine.• He stayed on at college for an extra year to do a Master's degree.• Forty-four per cent of fifth formers now choose to stay on at school.• The others went back to the hotel, but I stayed on in the bar, chatting to Alan.• I'll be late home -- I'm staying on to help organize the exhibition.• He entered University College to study zoology and stayed on to work in genetics.• It's okay, I'll stay on until you're ready to leave. 