For example, in the key of c sharp minor we would normally have a d sharp. But what if the given bass note is a d natural? How would this be notated with roman numerals and figured bass? Is it just a ii?
I think you are under somewhat of a misapprehension in regards to what a figured bass aims to tell you.
In essence, a figured bass tells you the underlying harmony in which the piece operates. It is very much melody agnostic and also tells you nothing about what chromaticism may have been used to make the music interesting.
It tells you the basis not anything about the beauty of the melody or the non-chord notes.
How would this be notated with roman numerals and figured bass? Is it just a ii?
It would still be the same chord with some sort of non-chordal note that acts as some sort of condiment to the main harmony, that is if it is indeed not a seventh of the chord (OR some sort of other note that can be construed as chordal.), then it would certainly affect the notation of the harmony.