Can an errant clause trip over the Christmas lights and bring a post-holiday sentence crashing down in disagreement?
The answer is trickier than you might think, but let’s work it through and see.
The sentence in question is imperative (a command or a plea) and is aimed at an implied you.
Now comes the tricky part. Does the clause that don’t work go with the noun string or the prepositional phrase of lights?
The writer thought it went with the prepositional phrase. If that’s the case, we could turn the sentence around and have it make sense: Of lights that don’t work, discard the string.
So the clause goes with the noun, the noun is singular, and therefore the verb should be singular as well:
Discard the string of lights that doesn’t work.
Next year you’ll know.