Someone asked a similar question but with a caveat of leaving the country-I don't plan to leave. How do I find out if my B permit is tied to my employer? If I quit, can I work with my B permit? If I'm fired? Also how does a B permit person get unemployment in CH? Thank you for the information!

Maybe this recent thread can shed some light:

NonEU one year B Permit - Quitting Job

Best if you read through your permit and describe it on here ( without the identifiers ).

I just picked up my Permit B today, and it clearly says on it that I can change job or profession (on the back).

Cool, what about Swiss unemployment if we quit or are fired? Also who can I call to get this info? Migration? Thanks all!

You cannot tell whether the permit is attached to an employer by looking at the non-EU B permit.
Mostly the Indian outsourcing companies do attach the permit to the current employer.
I have just been through this story very recently as I found new employment with the same permit.
My B permit is open.
You can call Arbeitsbewilligungen at 043 259 4949 to check.
This is for Kanton Zürich.

When my dependent-spouse permit changed from L to B my employer actually got a letter that confirmed my 'free' status - I think it was requested by my employer, but she kindly gave me a copy that I have carefully filed away...

Issued by the 'arbeits amt'...