These roots look dead to me, yet have green tips

[Roberta]

Even a dead root can help hydrate the plant by capillary action, and can also help anchor the plant in the pot for stability while it is growing new ones. So if a root doesn't come off easily with a tug, it is useful even if dead or moribund.

[estación seca]

I can't tell whether roots are alive or dead. I leave them on. If they are dead they won't cause further trouble. If they are alive you have damaged the plant.

[websherpa]

Originally Posted by Optimist

Besides what you see is velamen, the root is a fiber running through the velamen. In some cases, the velamen might be cracked, stained, or even burned by chemicals or too much fertilizer, but that does not mean the actual root is not working and taking up water.

This is an observation I made recently without really realizing what was happening. So perhaps a lot of people think of the air roots like I originally did.

In my Phals and Neos, I am now supposing the "velamen" is actually quite a thick layer and can exist and function even if "broken" but still attached by the root vein.

I had some roots with velamen rot but noticed that each end between was connected by a harder but extremely thin vein.

Until I decide to not cut, but repot and observe, I can now see (from it greening up, and continued growth of the root end), that the thin vein is actually the root and continues to supply the plant from further along the root. Being quite strong, by comparison, I would imagine it also serves the function of maintaining a hold on the plant's environment, and the velamen serves as a secondary moisture/growth storage system.

This is really just my casual observation, I haven't ever read or researched it that way before. But it came as a surprising revelation to me as I had always thought of the thick air roots as "the roots" - since the thin internal vein is easy to dismiss.

[Orchid Whisperer]

That "vein" is called the stele. And you are right, that is the functional live root. You can think of the velamen as more of a "water bottle" that you can refill. Frequently, a live stele that has no velamen can connect sections of root that do have live velamen.