Holding L1 and H4 at the Same Time

My husband is working at USA. He has a H1B visa. I would like to join him at USA. I am a L1B visa holder. But there is no opportunity for me right now to work at USA. I would like to know whether my H4 can be processed without my L1 getting cancelled. I just want a change of status from L1 to H4. Later on if my company can find me work at USA, I would like to change my status from H4 to L1.

It is up to the officer if he wants to cancel your L1 visa when issuing an H4.

Remember there is a time requirement for work outside the US for an L1 worker. If you meet the requirements and the job meets the requirements, you employer can file for a change of status from H4 to L1B. He would need to do that anyway or you would have to exit and reenter on an L1 stamping.