With adjectives that denote something changed in some way (especially past participles), un- is productive: you can use it freely to indicate that the change hasn't happened, or has been reversed):
uneaten; unfinished; unpainted; unedited.
With other adjectives, it is fairly common, but not paticularly productive: there is a more or less fixed list that it can be applied to:
unhappy; unwelcome; unenergetic. But not normally *unangry; *ungreen; *undifferent.
With verbs, until the advent of computer interfaces, un- was pretty well limited to verbs of enclosing, attaching, or fastening:
unwrap, undo; unbutton; unlock; unbuckle; unfasten; unload.
But now that computers have made many more actions reversible than are so in the real world, there are many new coinages:
uncheck; undelete; unsubscribe.
Edit to answer your specific question: I can't imagine what you might mean by "unparse", as it parsing not a reversible operation as far as I can see. But if you can find a reasonable meaning for it, use it. "Unparsed" is of course normal, under the first heading of adjectives above.