@Jussi_Aaltonen It helped. Thanks a lot.
Recently I discovered that even QuadRemesh works with custom UV mapping so I really hope that with modifiers such as Edge Softening and Shut Lining it will be no different.
Custom UV mapping ES and SL all serve the same purpose - to achieve high-quality rendering meshes (without breaking your Nurbs model). So it will be a sad thing if those tools can’t cooperate.
Filleting could be all right if you are done with the development, and Edge Softening shouldn’t be compared with that. Filleting is a very precise, tedious and often complicated process and it is just for other, more serious stuff.
I understand that Edge Softening is not very important, but since it is here, it would be cool if we can be more sure that it will work, produce closed meshes and preserve mapping.