Great question! The answer is that, well, you don't, but that's not what I'm intending unstained to mean here.

As it turns out, "unstained" is structurally ambiguous, because English has two different "un-" prefixes, each of which has different functions and different category selection requirements.

The first attaches to verbs, and means "reverse the action of", e.g. un-tie, un-do, un-stain, etc. The second attaches to adjectives, and means "not X", e.g. un-happy, un-satisfied, etc.

So, if we want to form the word "undoable", we can either take the verb "do" and attach "-able" first, giving us an adjective "doable" to which we can then add "un-" to give us "undoable", an adjective meaning "not able to be done" ("Flying by flapping your arms is undoable")
OR
We can take "do" and add the other "un-" first, giving us a verb "undo" meaning "to reverse the action of something" to which we can then add the suffix "-able", giving us "undoable", a different adjective meaning "able to be undone" ("Simple knots are easily undoable")

So, while both of these look and sound like the same word, they actually have different structures that correspond to the differences in their meanings.

In my OP, you read "unstained" as "unstain-ed", with "un-" attaching to "stain" to give a verb "unstain" meaning "to reverse the staining of", and then added the participle suffix, while my intended structure was to attach "stain" and "-ed" first, giving a participle (adjective) "stained", to which we can then add the other prefix "un-", giving "un-stained" "not stained".