You and your coworker are both really busy at work today. You worked later than usual, but now you're going home. Your coworker is still working. After you tell her that you're leaving, you say:
Don't stay too late!
In spoken English conversation, you say "stay late" to talk about staying at work until later than usual, or later than other people.
When you're writing or speaking about it in a more formal situation, you can say "work late" instead.
This is a friendly phrase to use when you're leaving work and your coworkers are still working.
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