For example #3 you need to say "THAT I have forgotten..." or equivalently "THE FACT THAT I have...". Besides quoted speech like in your first example, I don't think you'll find what you're looking for. But maybe I'm wrong. Who knows everything.

1. "I love you" is often heard these days. Here the quote "I love you" is indeed a complete sentence that is the subject of another sentence. 2. This is only one sentence - the subject is issue, and the verb is 'is'. Stripped of all other considerations is a clause that ideally should have commas around it. 3. This is incorrect as is. A correct version might be: I have forgotten to lock the door which could make them angry. This is only one sentence - I is the subject, have forgotten is the verb. Which could make them angry is a clause.