Cattelaya concerns

[Leafmite]

I have bought many Cattleyas that have a root system just like that. They always recover. Thankfully, you have a new growth starting and even a root (Mine are usually not as fortunate).
Here is what I do: I get a basket pot and either red lava rock or LECA and fill it nearly to the top. I remove all the dead roots and then I stake it on top of the medium (I wouldn't bury the new root, either but let it bury itself) so that it doesn't wiggle. Put the pot where it doesn't need to be moved for a few months. The new roots will grow down into the medium and anchor the orchid. By putting it into LECA/red lava rock and a basket pot, you are allowing more air around the roots which will help prevent rot. By not burying the living root, you do not risk harming it.
Good luck!

[1flower1world]

I am sorry if I had gone too far on this subject. The plant in question is in a very bad condition. It is not easy to repot it with only one single fragile root. Mounting it would be another option if the growing environment is suitable.
Last year I mounted a rootless "nobilior tipo" (with three wrinkled bulbs and two crinkled leaves) on a cork bark. Today, the plant recovers a lot (see pic). The once wrinkled bulbs are fattened and the once yellow leave is turning green gradually. There are two new growths though they are much smaller than the old ones. The plant survives!

[silken]

I agree, if the person can give it good humidity and knows how to mount it in such a way to make it stable, it is similar to Leafmite's idea of setting it on Leca balls and letting the roots grow into the media. It can work.