I have moved to Switzerland with my company. I hold an EU passport and as such, I have just been granted a B Permit.
My fiancée (Non EU Passport holder) and her child (who is an EU Passport holder from the father as he is an EU Citizen) have moved here with me and are currently applying for their permits via a Family Reunion Visa, as advised by the Swiss Authorities. For clarity, we are not yet married and do not intend to get married within the next 6 months. The child is now in a Swiss local school.

I have the opportunity to now get a better job position outside of the EU. That would mean my moving overseas away from my fiancée and her child. She has been advised that a B Permit is the suitable permit achieved from a Family reunion application – that’s not the main point of my question, though it would be good to get feedback from somebody who has applied under Family Reunion.

The main question is: If I leave and start paying Tax in another country, is it obligatory to inform the Swiss Authorities and have them cancel my B Permit, or can I still be employed overseas and hold that B permit for some time?

Secondly, if my B permit does eventually get cancelled, what will happen to any application for my Fiancée - and can she hold a B Permit applied under Family Reunion, if I have mine cancelled.
If her Family Reunion application is cancelled via the process above, what Permit can she apply for that will allow her to stay?

If you are moving out of Switzerland then you should deregister which cancels your permit - and will cancel her application as well.

If you don't deregister then the permit will expire after 6 months - and again her application with it.

For family reunification all the family must live together in the same location - which won't be the case if you're living/working elsewhere.

Her permit is dependent on you having one. If you don't, then she doesn't either.

There is no permit she can apply for on her own since she is not employed by a Swiss employer. Non-EU nationals can only get independent permits, i.e. not via family reunification, if a Swiss employer applies on their behalf and proves they can't find a Swiss/EU national to do the job.

Easiest solution is for them to move with you to wherever you're going, assuming the father of the child is okay with that. If not, then you have problems.

I'm not sure this is going to work out very well. If you're not married and have no plans to marry, then your only option (assuming the canton offers it) is a concubine permit. Medea can go into the details.

Pretty similar to family reunification. You'd have to agree to be financially responsible for her for 5 years, even if you break up and she stays in Switzerland. But you have the same problems as with family reunification - you all need to live in the same place together and if you don't have a permit, neither will she.