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Wiktionary
stay on

vb. (context idiomatic English) to continue in a place or situation, while others leave.

WordNet
stay on

v. continue in a place, position, or situation; "After graduation, she stayed on in Cambridge as a student adviser"; "Stay with me, please"; "despite student protests, he remained Dean for another year"; "She continued as deputy mayor for another year" [syn: stay, continue, remain]