The employer can eliminate existing positions (or staff) and then create new positions and require staff to reapply for them. They should not be able to consider the failure  to reapply as a voluntary resignation for unemployment purposes, however, if they first eliminated the old positions: that is, if they eliminate your position, you have been terminated, not for cause, and should be eligible for unemployment compensation. Arguably if you don't then apply for an available and appropriate job, you could be violating your obligation to seek new employment--but again, it should not be considered a voluntary resignation if, as a matter of timing, the old job is first eliminated, which is an involuntary separation from work.On the other hand, if they don't eliminate your old position first (but rather have you apply first), then a failure to apply for the new position would be considered voluntary resignation, since you are choosing to not take a step to preserve employment--though if you apply and are turned down, you'd certainly be eligible for unemployement. Therefore, the timing and exact mechanism of what the employer does is critical.