Create a new Shader, use the texture in question as Diffuse and as SelfIllumination and create, import and use a texture that is transparent everywhere but where you want the original texture to be unlit.
Go to your texture browser and click File -> New. Select Shader (should be selected by default), enter where you want it saved and click ok. Open the properties of the newly created Shader by finding it in the texture browser -> rightclick on it -> select Properties. Keep this window open and move it to the side.
Search for your texture now and select it. In the Shader-Property window "use" the selected texture as Diffuse and as SelfIllumination. Without a mask applied the whole texture will now be unlit.
Now open your graphics program and create a texture with the same resolution as the original and make it transparent everywhere but where you want the original texture to be unlit. Save it (for example as a .tga). In the UnrealEd texture browser go to File -> Import -> search for your newly created image -> enter package details and check the little box that says "Alpha" or else the transperency channel will be ignored.
Now select that new texture and "use" it as a SelfIlluminationMask in the Shader Property window.
Note: Don't forget to select the "SurfaceType" for the Shader so the game can play the correct foot-step sounds if someone runs over it in-game.
Note 2: Never "use" the Shaader in itself. Ie, never open the Shader's Properties and just click "use" without selecting another texture first. This will crash UnrealEd.