Linux is a kernel which is often bundled with proprietary components. Android, for example uses the Linux kernel. The whole desktop operating system you seem to be thinking of is a Linux distribution.
There have been many Linux distributions with proprietary components over the years. SUSE’s YaST configuration tool used to be proprietary, for example. There’s probably something current along the same lines, but there’s not much demand for semi-proprietary desktop Linux.
I don’t know where you live, but it is not normal for prospective employers to ask for your medical history most places, and is legally questionable if not outright banned under the anti-discrimination laws of many countries.