It is not the EAD issue, it is the status issue. If the L1, J1 ......etc left the US for visits (which I do not think is your case) and his/her status is active, then the dependents can follow their regular activity in US (work with EAD, study with the dependent visa ...etc). But, if the principal visa applicant finishes his mission and his status gone (either by finishing the whole time on that visa or prematurely terminated it by resignation or terminated by any way or the other) then, the dependent status will be dropped too and any privileges based on that will be dropped including the EAD. Remember that the employer is the primary beneficiary, the principal (e.g. L1) is the secondary and the dependent (e.g. L2) is the tertiary and the later is the most vulnerable to any problem in this chain.