If your spouse only goes back on a brief visit to India, intends to come back well within the validity period of his L-1B visa and otherwise maintains status, then yes., you can still work during his temporary absence from the U.S.
If, on the other hand, he left with no intent to return, then no, since you status is dependent on his.
Behar Intl. Counsel 619.234.5962 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.
It depends on whether your spouse is going back for a short visit or not. If he is going back for a short visit, you can remain in the US. If he is going back for a long period of time, you cannot remain in the US.
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.
As long as your spouse and his employer expect to continue their relationship, and foresee a continued need for his employment in the US as an L 1, and continue to renew his L visa, there is no problem with maintaining L 2 status and renewing your EAD, no matter what the length of his absence is.