Theon defines prosopopoiia as,
"the introduction of a person to whom words are attributed that are suitable to the speaker and have an indisputable application to the subject discussed." (Theon 115, Kennedy).Key here are the two qualifications, namely that this speech should be "suitable to the speaker," and that the speech "have an indisputable application to the subject."
Theon then gives several examples, from very general to very specific. For example, "What words would a man say to his life when leaving on a journey? Or a general to his soldiers in a time of danger?" Or, more specifically, "What words would Cyrus say when marching against the Massagetae?"
As you can see, one can create a variety of persons and situations and then create a speech to be given by that person on that occasion.
The Greek historian Thucydides, recording the way in which he reconstructed historical speeches, admitted that he took some liberties, and essentially recreated the speeches according to the rules laid out by the preliminary exercise of prosopopoiia. Thus, even in Greek History, it was acceptable to take some liberties in recreating historical speeches. Thucydides writes:
And as for things that they each said by way of argument, either when they were about to go to war or when they were already at war, it was difficult to carry the precise details of the things that were said word for word in one’s memory. This was the case both for me, where I heard them myself, and for those who reported them to me from various sources; but they have been rendered in the way it seemed to me likely that each speaker would indeed have said what was needed concerning the present circumstances on each occasion, while sticking as closely as possible to the general ideas behind what was actually said. (Emphasis in bold is mine. Thucydides, Hist. 1.22.1-2).There are many speeches in the New Testament. Many have speculated about the speeches in Acts and to what degree Luke was reporting the actual speech, or rather, engaging in prosopopoiia, creating a speech in line with the character of the speaker and in line with the needs of the situation.
One good example of prosopopoiia in the gospels comes from Jesus' parable of the rich fool. Jesus creates a speech for this rich fool, as the rich fool actually has a conversation with himself. Here is the relevant section from Luke 12:
Luke 12:17 And he thought to himself, ‘What should I do, for I have no place to store my crops?’Creating this speech in character creates a liveliness to the parable. The implied question behind this parable for which the Lukan Jesus creates a speech is, "what would a rich man say if he had a surplus crop." Then comes this speech where the rich fool has a conversation with himself.
Luke 12:18 Then he said, ‘I will do this: I will pull down my barns and build larger ones, and there I will store all my grain and my goods.
Luke 12:19 And I will say to my soul, ‘Soul, you have ample goods laid up for many years; relax, eat, drink, be merry.’