I am currently on L1B visa in USA. Visa has expired, I 94 valid till Feb 2014. I have filed for L1B to L1A conversion. In case I get a rejection after my I 94 expires, can I file a change of status to H4 after I 94 expiry? If yes, can I also apply for change of status to H1B visa in the April 2014 quota. How can apply for H4 and H1 ensuring that I remain in USA and on legal status?
No, it cannot be done. For COS to be approved, the I-94 needs to be valid at the time of filing. If you have concerns about L1A COS rejection, then start the H-4 COS now before I-94 expiration.
You will have to watch out for Last Action Rule in this case as you will have two active COS happening.