I recently brought in a wire that was left outside. I went to use it, but when I stripped 8 inches of sheathing off, I realized all of the cardboard inside was wet, so I stripped the outer sheathing off of the cable until I found a dry part. Most of the cable was wet, but the individually insulated conductors looked fine. The part that was dry still worked fine. Is it safe to use the individually insulated conductors from the romex wire inside conduit?

Over here, it is standard to use single isolated wires inside Plastic conduit, when installed in a way that it can't be damaged (like inside a wall) and the conduit is complete between the devices it connects (no place where there is a gap in the conduit). That's with "pipe" conduit, not with raceways with removable coves. The wire is available to buy as single wire (of each of the standard colors), but is otherwise identical to what you might extract out of a cable

However your codes may be different...

Also, Water can soak into the single wires too, between the Copper and the isolation. Strip the wire and see whether there is any sign of oxidation (color change) on the conductor, and if there is, how far in it goes

Anyway, give the wires a good long drying in a warm dry place so that any residual moisture trapped in microcracks in the isolation etc would get out

I recently brought in a wire that was left outside. I went to use it, but when I stripped 8 inches of sheathing off, I realized all of the cardboard inside was wet, so I stripped the outer sheathing off of the cable until I found a dry part. Most of the cable was wet, but the individually insulated conductors looked fine. The part that was dry still worked fine. Is it safe to use the individually insulated conductors from the romex wire inside conduit?

While the wire maybe in good condition and fine to use however it is a NEC violation as the NM (AKA Romex) cables individual conductors have no labeling (wire gauge temp/voltage & other required markings) rating for conduit purposes you will have to use THHN/THWN or other marked & labelled conductors. As always it is your call the individual maybe fine and safe to use but if the work is it be inspected it will fail because of what I stated before

It is not good idea. First the insulation of the individual wires from a cable may use different material and design (thickness,...) than the one used on single wires designed to be used in a conduit.
So it may lack some environment resistance: Could be more ghygroscopic, may lack the overload heat sinking capability (gaps between the wires in a cable used to be filled by a sort of goo, which is able to take quite a lot of surge heat energy by melting itself, so keeping the conductors safe mainly in the short circuit overcurrent faults, individual wires need this robustness in the wire insulation alone).
And even when some cables could be assembled using the same wires as designed for bare use, stripping the cable may damage the insulation or the conductor (fatigue stresses, work hardening and consequent brittleness,...).
As a result you are more likely to get problems, include fire hazards or so.

The missing labeling is then just a minimal problem compare to others. But it is a tell-tale sign, so sought after by inspectors (among others, like characteristic stripping scratches,...).

And by the way: If the paper layer was wet, so will be the insulation plastic. It may not seem so, but most plastics likes to be quite hygroscopic, unless really explicitely treated by quite expensive additives to not be. The humidity may not seem obvious, but e.g. with PVC it tends to trigger the release of the chlorine, causing severe metal corrosion in quite a short while.
So use only the section that was dry and as a complete cable. Assuming the cable was rated for wet environment (and the water gog in only from its unprotected ends).

Inside metal connection boxes (or devices like Fluorescent luminaire), the single isolated wires of the supply cable can make contact with the metal body of the box. This is equally true for single conductors coming from a conduit or from a cable. There aren't any special instructions for protecting the single isolation wires of a cable from contact with the enclosure from inside. The single isolation is fully trusted (for class I in this case)

And if it is, then it is sufficient for contacting Plastic conduit as well