I don't recall this being a thing, can you link to any documentation about it?
Words like textures are pretty vague so I just get results about things like the "detail textures" setting that was common back then or about the alternative high quality textures they included in UT GOTY's 2nd disc for use with cards that could support the new S3TC compression technique.
Here is a texture where this is very noticeable (zooming with the camera, that's 3 different pictures, you can tell from the text on top):
As you come closer to the texture, a new one (the cracks) is loaded and fades in. Those cracks where not there from a certain distance. You can see the fade-in when you are in motion.
This happens with the majority of textures in the game. Each one has a different "detailed texture" that fades in when you go close. Wooden floors in particular look very nice with this, almost like a modern game.
This is with the default textures, not the S3TC ones. But i remember back in the day, not all APIs supported this. I could only see it with a Voodoo 3 card and Glide. A friend who had a TNT card couldn't see this effect. I don't think modern cards support this by default either. I had to download a custom dll file for this to work a while back (evidently, it still works).
Unreal Tournament 1 is the only game where i ever saw this, personally.
Edit: Here's how the textures (in this case, wood) would look with a non-glide card back in the day:
And here's how it would look with Glide or the custom dll:
Both instances would look the same until you stick the camera on the surface (the slightly different color is probably the same texture on a different area and lighting in the map). Those fine details n the second picture would fade in, as you get closer, almost like a second texture on top of the regular one. Can't explain it differently. I mentioned UT is the only game where i saw this and that's mostly because of the way this detail fades in and out.
Again, this happens with all textures in the game, without using the second disc that had a bunch of HD textures that only replace a few of the default ones.