My wife study(master degree) at EPFL and I am working with an open contract via dependent B permit. We are both non-eu. I wonder if she graduate from EPFL and cannot find a job, can we continue our permits with my open contract without my company sponsor it?
No, your right to live in Switzerland is tied to yours. It's not possible to switch from a dependent non-EU permit to an independent one unless your employer re-hires you as if you were a fresh non-EU hire (along with "proving" to the cantonal labor authorities that no Swiss/EU candidate could be found for the job).