He/she is not required to stay in the USA, especially since he/she does not currently have status. However, abandoning your asylum application (or any applications) can potentially bar you from entering the USA for a defined time.
Yes, you can voluntarily leave the US, but before you make this decision, which will probably eliminate any chance of ever coming back to the US, you need to at least have a consultation with an experienced immigration attorney. Good luck.
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You are free to leave at any time. It might make sense to draft a brief letter to inform the USCIS that you want to abandon your petition, in case you wish to return someday.
The above reply is not actual legal advice and should be construed as such; this reply does not constitute an attorney client relationship and is offered only for general informational purposes. Please consult an attorney for more detailed and personalized assistance.
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