Since she left the employer that sponsored the L visa, technically the EAD that was derived from that sponsorship became invalid. Therefore, she should reapply for her EAD based on the pending asylum case.
This is not legal advice and a client attorney relationship is not created.
Given that your wife is no longer in valid L-2 status due to your no longer being in valid L-1B status, the EAD she now holds has been invalidated by operation of law and can no longer used. She should apply for a new EAD based on your pending asylum application, as a prospective derivative asyleee.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.