That does tend to happen to vinyl automobile upholstery and dashboards over time. The plasticizer is a high boiling point oil, but it still has a vapor pressure and will slowly evaporate. High temperature, vacuum, and large surface area will accelerate the process. I don't think that this would ever be economically feasible.
Potentially you could run it through an extruder and apply a really good vacuum to suck off the plasticizer. It could actually work. I know that it is possible to remove water from plastic in that way.
I had to look at notes that I kept for four decades, we did extraction of PVC resins with methanol in the lab. Acetone was used to clean plastisol formulations from mixing bowls.
All the above suggestions will work but I doubt you will ever remove all of the plasticizer as they are designed to like the resin and diffusion laws apply. You could probably remove it to the point most couldn't tell there was any left but you could detect it analytically.
