Single-word sentences are fine, because subjects and predicates can be implied.
If we were driving in a car, and you kept singing an annoying ad jingle over and over again, I might say, "Stop!"
"Stop!" is a one-word sentence. The subject (you) is implied. It's essentially a shortened version of, "Will you please stop singing that song!"
Contextually, it would be obvious that I was asking you to stop, not the car. It would be obvious that I was asking you to stop singing, not stop breathing. Hence, I don't need to add those words, just to make it a sentence. I simply yell, "Stop!" and you figure out the rest.