Is it possible to create a single overlay that doesn't move with the map?

[Matt]

I'm trying to create an overlay that sits above the map tiles and below any markers and controls. It needs to be statically positioned - not pan with the map. 

I'm trying to create something akin to a loupe where most of the map is obscured by a darkened tint while a small portion isn't. I've looked into tile layers but I don't see a way to create one that doesn't pan. I've also looked at simply placing divs over the map but that obscures the markers and controls and makes them inaccessible.

What's the best approach to do this? Has anyone seen an example of a static overlay in the wild?

[Kesuke]

Does your map have a fixed width/height or is it fluid?

[Matt]

It's fluid but I have observers on window resize to handle it's layout (particularly vertical) so any solution that works fixed/width should work fine fluid. Why do you ask?