It is illegal to work in UAE during visa transition period

We assume that your husband is changing his employment within the UAE. An individual in the UAE can only take up employment if he or she has a valid employment visa. In this instance, you should hold an employment permit (labour card) issued by the Ministry of Human Resources and Emiratization in the UAE. 

Since your residence visa is cancelled, you should inform about the same in writing to your employer. Under the UAE federal residential laws, you should not work during the transition period as your visa is cancelled. Once your new residence visa is issued, you may resume work with the same employer. Further, if there is a delay in the issue of residence visa to your husband, you may obtain an employment visa from your employer.