Given that your wife does not have a legal status, I would strongly recommend that you talk to an immigration lawyer to see if it is even prudent to apply. A good attorney should be able to talk with you about the process and whether you need help or not.
If she is legally eligible to apply for adjustment, the work permit is based on having that application pending. It does not reference her prior or current (lack of) status. In most cases, the appropriate box is (C)(c)(9).
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Generally you should put c (9) since she is filing her green card pursuant to her marriage to a US citizen. It is best to consult an attorney before filling all the paperwork to avoid delays.
Alexus P. Sham email@example.com (917) 498-9009. The above information is only general in nature and does not constitute legal advice. It does not create an attorney-client relationship.
An I-765 can only be filed if an adjustment of status application is being filed with it or is pending.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.