UV coordinates scale with changes in object scale? Right now, scaling a textured object like this one:



By a factor of 3 on the X axis, results in the following:



I would like the same scaling operation to produce these results:



In other words: I want the UV coordinates, not the texture mapping in existing UVs, to scale with the change in object scale. I tried the UVproject modifier, but has it to be applied manually. I want the UV rescaling be done in a fully automatic way.

Is there a way to do that in blender?
You can try to use Vertex Slide instead of scaling.
Select the vertices / edge you want to transform and hit 2 x G or Shift+V to Vertex Slide. Move it to desired location and make sure you have Correct UVs checked in the options (left T panel).
You can use keyboard to set the exact value while sliding (I set -3 in the video).

If you need to extend the vertices outside, start sliding and keep Alt pressed.