Does freedom from birth and death mean there is no freedom to experience birth and death without desire?

As I understand the cycle of birth and death produces suffering but ,once the truth is realized, there is no suffering ,so living in this world shouldn't be any longer a problem .So is freedom from birth and death here mean only that there is no binding to the cycle or that there is no longer a possibility of experiencing the cycle forever ?. This may induce another question if one can be reborn fully aware of the truth ,if that is no-longer a possibility then how can this be considered true freedom ?.