Must a desiccant be made anhydrous before it can be used for drying?
In the oil and gas industry, glycols are used in a scrubber to remove water from natural gas [methane] for a number or reasons: water is very soluble in glycols, water is extracted into “dry” glycols due to equilibrium forces, and there is efficient contact between the gases and the liquid.  Another huge part of the stribber is the regeneration portion of the system, the stripper – getting to the point of your question.  Heat is applied to the water/glycol mixture after having been in contact with the “wet” methane, driving off the water and regenerating the sorbent, the glycol.  The glycol can then be recycled.  Although I have described this as a batch process, the actual process is continuous.
In an industrial setting, “throwing something away” is used as a last resort.
Below is a schematic of a glycol dehydrator and regeneration unit.

https://www.sciencedirect.com/science/article/pii/S2352484719301039#fig1