Morality play central characters face a conflict: whether to choose the path of righteousness, or the path of evil.
The character of Faustus represents the stratum of society which is vulnerable to fall into the temptation of seeking knowledge above spirituality, resulting in uncontrolled ambition. In this way, Faustus illustrates a morality play character. Given that Faustus chooses to follow the path of evil, this is, eventually, his downfall. The morality character ultimately learns his "lesson," and warns the audience from acting the way that he did.
Conversely, Doctor Faustus fails to be a complete morality play character because he does not succeed in changing. He does not learn his ultimate moral lesson. He becomes scared of suffering the consequences of dealing with a demon, yet, he does not find the courage and faith to accept God's grace.
My God, my God, look not so fierce on me!
Adders and serpents, let me breathe a while!
Ugly hell, gape not! come not, Lucifer!
I'll burn my books[to keep Lucifer away]!—Ah Mephistophilis!
If Faustus were a true morality play character, he would have been convinced by the other allegorical characters to repent and accept God's mercy. This would have rendered him penitent, then forgiven. Not so for Faustus. Nothing positive turns him from fear to accepting forgiveness.