If you mean strictly nouns, then there are lots of counterexamples with pronouns:
I heard you!
She doesn't care.
If you are lumping pronouns in with nouns (not usual, but I can see you might) then examples are rarer, but they exist. Besides the imperatives that jknappen mentions, in informal conversation you hear things like the following:
These are clearly formed from "It depends", "Do you think so?" and "I haven't been", but while they may not be formal English they definitely occur and any practical grammar of English needs to account for them.
By the way, from your description, it sounds as if you are regarding a sentence as a string of words (when you say "either before or after a verb") That approach to NLP simply doesn't work: you need to consider structures, not just the surface string.