Last I checked, the noise modifier doesn't modify the UV's. Textures stretch because the geometry is stretched away from its original mapping. You're mapping the same number of pixels to a distorted area. If you wanted to avoid that you'd somehow need to compensate in the texture map by altering the fidelity of the…
Fixing unwrapping by hand would take hours. You're right I don't want to freeze vertexes on UV map. I'd like them to be moved along with geometry deformation made by noise modifier (the same as checking "preserve uv" in polymodeling option in 3ds max. But I found a solution. Exporting original model to zbrush and deformed…