This plant is Dracaena marginata.  [D. reflexa][1] or pleomele reflexa has shorter thicker leaves.  Root rot is extremely common with these plants as they are used to high light and a dry environment.  To diagnose whether the plant is worth saving:

- grasp the stems.  If they are firm the plant will  but out of old growth if you place in a high light environment
- if the stems feel hollow then the xylem/phloem is dead and the plant is beyond saving

I suspect this is root rot.  If it was cold damage you would see wilting at the edges and tips of the leaves.  Root rot happens from the bottom up for this plant and the dead material at the stem indicates this.

Removing the soil and washing the roots is quite traumatic for most plants so I would avoid that in the future.

  [1]: https://en.wikipedia.org/wiki/Dracaena_reflexa