Thing that does not dry in sunlight

Ice

Ice can dry things (removing moisture by freezing it), but in the sun it would melt, becoming less dry (more wet).

Skin

Same explanation as ChronoDs answer, but I think this is what is actually drying.

Wine!

Explanation:

The sweetness and dryness of wine is determined on how much of the sugars from the grapes are consumed by the 'yeast beasties'. The more sugar they eat the dryer the wine.

If the temperature is high it can cause the yeast to die and thereby leaving the wine sweeter.

In sunlight, temperatures would rise and the yeast would die making the wine sweet and not dry. Therefore, to answer the question, only in shadow does it become dry not in sunlight.

(If nothing else - at least we are slightly more educated now :-] )

Another possibility, this one I quite like:

The plastic film of solar still

Because:

• When the sun is shining on the still, water from the surround ground evaporates and condenses on the plastic film. This makes it wet.

• When in the shade the still cools down and the film dries up - any water drips of it and because the still is cool there is no more water condensing on it so it dries out.

Perhaps something like:

Mercury

Because

Mercury is a metal that is molten (liquid) at room temperature. So in the sunlight it will melt. If you stick it in the shade it will cool down. If you get it cold enough it will solidify which is sort of the same thing as drying out. You have to use the term "drying" quite loosely as technically drying is the removal of a solvent causing something to go from liquid to solid.

Granted it would probably have to be on another planet to do this as I'm not sure there are many places on Earth where the temperature differential between sun and shade would be enough to cause mercury to transition between solid and liquid. But coincidentally if you somewhere like on the planet Mercury, the difference between a shady place and a sunny place is hundreds of degrees.

Wood (Trees)

Because

the sun actually let's it stay alive, but if it is left in the dark too long, it will die and dry out. (And, yes, I know that technically water is the factor here, and there are plants that do thrive in the dark...)

Is it a

raincloud?

It only dries up when it's rainy outside.

With mountains, the leeward side can have a "rain shadow", where it is dry, as the moist air mainly stays on windward side. So, in the shadow, it is dry, and out of the shadow, it is wet. It's just that it doesn't necessarily have to be in the sun to be wet or dry, nor is there really any specific "thing" that is getting wet/dry, unless you count the air or something :/ I don't really know, that's as far as I got with this...

Still new to the site, my answer is a wet mobile phone. Because to completely dry it you immerse it in rice to suck out all the moisture. Essentially hiding it in the shadows away from the sun. I know its not the correct answer, but it is fitting to the requirements thought i'd give it a shot.

The obvious one to me would be

The air. Just think, the typical process of drying is though the evaporation of water from a surface into the air.

The tears of a person with severe agoraphobia