The expiration date on the I-94 card is written on the card usually around the stamp with your entry date. If you are out of status you should speak to an immigration lawyer to make sure what your applying for is correct.
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The I-94 is the arrival/departure card that was given to you when you arrived. See what was on the asylee/refugee document -- did you enter as a refugee or as a nonimmigrant traveler and sought asylum when in the U.S.?
An attorney-client relationship is not formed by my responses to questions on Avvo. My responses are not intended to be legal advice and must not be relied upon as legal advice.