How does the caramel in creme caramel stay liquid?

There is not supposed to be liquid caramel sauce in creme caramel. You pour the custard on top of the caramel to bake it, and in the oven, the custard dissolves the caramel. Since the whole package is not being disturbed, the dissolved caramel doesn't mix in the whole custard, instead you end up with a bottom of caramel-tasting custard and upper layers of custard without caramel. You get a tiny bit of exudation that lets you separate the custard from the baking pan and lets the surface feel slimy, but that's it. If you have a noticeable puddle of brown liquid on the bottom, you have overbaked your custard to the point where liquid separated out of the mixture and flowed down onto the caramel.

If you enjoy this state of the dessert (very firm, somewhat grainy custard shot through with channels, sitting in a puddle of caramel liquid), then you can go for it, but there is no reason to add any water to the caramel. Instead, just bake it to a higher internal temperature, about 90 to 93 C should be enough .

Adding water beforehand won't accomplish anything and will indeed probably be harmful for this kind of result. If you put dissolved caramel on the bottom of the pan, it will mix up too much with the custard, not leaving enough caramel for the whey to dissolve when it exudes. So you will have a thicker, but less concentrated, caramel tasting layer, sitting in a liquid that has a less caramely taste.