Hi there, 'to stay behind' suggests that someone has stayed somewhere specifically after the event has finished, or after everybody else has already gone home. 'The teacher stayed behind after class.' 'I stayed behind after the conference to speak to the speaker.' 'I stayed behind at the party to help clean up' To stay somewhere can mean that the event is still continuing, so if you take the party example you can say: 'I stayed at the party because it was still busy and I didn't want to go home.' Hope this helps!