changing jobs on work permit

My girlfriend is a filipina foreign worker.
Due to circumstances that I won't get into here she is out of work but received a new work permit valid another year but only for her previous employer.
She is currently on EI pending finding a new job.
She has been offered a job with a new employer .
My question is this: once the LMO is approved under her name and she has applied for a changed work permit does she have implied status allowing her to work for the new employer?
It seems wrong that she should stay on EI when she has the offer to work (and desperately wants to) considering that citizens are obligated to work when on EI if offered a decent job. However the cci website clearly states "do not start your new job prior to receiving your new work permit". I am well aware of so called agencies charging people sums of money for a new job that is workable while waiting for the permit...all illegal of course...at least I assume so.

Somebody please offer opinion