Can I refuse a demotion and be paid unemployment?

First of all, unless your current job/position is guaranteed by a still-in-effect (unexpired) contract for a definite or defined term (e.g. a one-year, two-year, five-year, etc. contract), you cannot refuse the demotion: you are (without a contract) an "employee at will" and may be demoted at any time for any reason without any recourse. So whether you sign or not, the employer may make this happen (or simply fire you).
If you state you refuse and the employer therefore terminates you, or you are demoted and quit due to the pay, etc. cut, there is a *chance* you might be eligible for unemployment benefits on the theory you were "constructively," or effectively fired, by your job becoming such that no reasonable person would do it (essentially); however, this would be more likely if your hours were staying the same and you were taking a 1/3 pay cut, so you were working as hard for a third less money. Even then, it's not definite that this would be considered constructive termination, since employment (in the absence of a written employment contract) is employment at will and the employee has no guaranty of any particular wage or right to not have a pay cut; the presumption in this country is that the employer *may* cut your pay and that is only rarely overturned to allow unemployment benefits, in the most egregious cases. And if your hours are being reduced to, it is *very* unlikely you'd be eligible for unemployment, if the reduction in pay is more or less commensurate with the reduction in hours: since employers can absolutely reduce an employee's hours, if the pay cut laregly flows out of working less, that would not be constructive termination. Your best bet may be to take the reduction while looking for a better job elsewhere.