Interesting situation. I assume your asylum case was pending for a very long time with no result and you were notified of the admin closure. If all you have is an admin closure, then you still have not been granted asylum status and cannot apply for you greenc ard, although you can work. I think this question can benefit from clarification from my experienced colleagues.
Either consult an attorney or if you want to do it yourself then read the instruction for 765. At the least you have a final order and can get EAD and if you are under order of supervision then again you can apply but you no longer qualify under your asylum application if there was no decision in court. Contact your last attorney for advise.
Yes, you should still be able to renew the EAD following admin. closure. Include a copy of the judge's order with the previous documentation. It is also worth consulting an attorney to ensure the proper code is marked on the I-765.
Attorney Khurgel is a former USCIS and State Department Embassy Officer. His comments on Avvo are general advice, and do not constitute an attorney-client relationship.
There is a distinction between administrative closure, which has happened here, and termination of proceedings. Administrative closure does not grant permission to apply for I-765 renewal, which was only available to you while your asylum case was pending. It is not, unless you have an attorney to move to be granted authority to apply for renewal. Termination of proceedings is available if you have an independent ground to apply for a green card, like through marriage to a U.S. citizen. Since you are still under the possibility of reopened proceedings by ICE, you could ask for supervised release, which could grant you permission to apply for work authorization.
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