I´m rather new to Blender and tried using the shrinkwrap modifier more, I can get it to work just fine on simple forms, but when there is a crease it always just makes a bridge as the closes vertices are not the ones in the crease. Is it even possible to shrinkwrap in a way so that a crease is not bridged over? If so, what would the setup of the Shrinkwrap be?
As Nand 27 says above, make sure you have at least enough geometry to work with on the source object. I have a plane that I subdivided so that it's about a 24x24 grid. Then, did you try different modes? For example, this is using the "Nearest Surface" mode:
But this is using "Project" mode, which projects onto the surface:
As you can see, in this case, the "Project" nicely follows the shape of the indentation, whereas "Nearest Surface" had trouble finding the corner.