As discussed in the comments, in the context of a headline, this would simply be a case of dropping forms of the verb to be (a common feature of headlinese): “The Centers for Disease control is/are announcing new precautions against the corona virus” and “Two more candidates are dropping out of the race today”.
When I first wrote this answer, I missed the fact that you in fact were asking specifically about spoken usage. I find it hard to interpret "The Centers for Disease control announcing new precautions against the corona virus" and "Two more candidates dropping out of the race today" out of context: do you hear people saying these as entire sentences? What are the preceding and following sentences? Depending on the context, "Two more candidates dropping out of the race today" could stand for "(There were) two more candidates dropping out of the race today" with conversational deletion of the first two words.
If the speaker is introducing a video or another speaker, The Centers for Disease control announcing new precautions against the corona virus" could stand for "(This is) the Centers for Disease control announcing new precautions against the corona virus".
If used as part of a longer sentence, the -ing words might be gerunds: "We'll be talking about the Centers for Disease control announcing new precautions against the corona virus". I assume this isn't the usage that you're talking about, but I'm just trying to imagine situations where people would say this, since it isn't something I've noticed.
Without knowing the context, I don't know what phenomenon explains the examples given in the question.