I refused a job transfer–now what?

I refused a job transfer–now what?:
Dear Evil HR Lady,I have been with my company for five years. Recently, I was told my job as department head was being eliminated but that I was being offered a new job at the same pay band. This new position would eventually report into the new department head, who would be brought in one [compensation] band higher that my current job. I say this move is a demotion. If my department’s new leader will be in a higher band that my current band, then my current job (which has an outdated job description) is under-ranked, and the new job they are offering me is a demotion. 
I argued for severance instead. They provided a draft severance package and gave me a five-day time frame to review it, after which the offer would be off the table. They have since relented by giving a few more days and said my lawyer can contact their lawyer if more time is needed. 
If I do not accept the severance package (a low-ball offer compared to their severance policy, which they claim I don’t qualify for because the new job I was offered is in the same pay band) and do not accept the new job, they will treat it as a resignation (documented in an email from HR). I have told them verbally that I will not resign. Is it possible to resign by refusing to accept a new job? To me, that seems more like a firing. Incidentally, I am in my 40s, female and black. Suggestions?


Note: In a email from HR, my company stated that I, as department head, am not doing the work the new head will be doing and that I am not qualified for the new head position. However, despite my asking, they have refused to show me the job description, objectives or qualifications for that new position.
To read the answer click here: I refused a transfer–now what?

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