How to achieve a thin caramel sauce/coating that stays fluid when refrigerated I want to make a caramel coating for cheesecake, or other cakes, that stays fluid in the fridge, and doesn't become hard/solid.

I don't mind if the caramel sauce/syrup contains any butter/milk or not; if it's only made by sugar and water is OK.
I made a caramel sauce, which was fluid for some time, but when I coated the cheesecake and put in the fridge, it became solid and I just sticked this out and threw it away.

If you have a recipe for this I would be glad to hear about, just as long as it is caramelized sugar, not clear syrup (slightly heated water plus sugar).
If you make caramel acidic, it won't harden. So use cream of tartar (neutral taste) or lemon juice (easier availability) to create a non-hardening sticky caramel fluid. 

I am not sure if you can add dairy (milk, cream, butter, etc). to acidified caramel, but there is a small chance that it will curdle, so I'd advice you to use clear caramel (browned sugar and water only). 

I don't know how much acid you need to keep caramel at a certain viscosity at a given temperature, you'll have to experiment for that. Or maybe somebody else can supply this information. IIRC, a good starting point is a tablespoon of lemon juice per 100g sugar, but this is very imprecise. 

The other option would be to make a semifluid sauce (cream, or starch-thickened milk, or diluted syrup) and add caramel to it, but the taste would be much weaker. My preference would be the clear caramel + acid route.