There is more than one Crooked Man; everyone suffering from severe depression has a Crooked Man of their own.
There is a note from an otherwise-unrelated man who killed himself in order to get away from...something. David also says that he's been hearing "voices" in his head, long before the Crooked Man started coming for him. The Crooked Man he keeps fighting is Duke's, but he's had one of his own for some time and it's part of the reason Duke decided to step in, figuring that David would know how to better handle his own when faced with someone else's. It's even possible that it was David's Crooked Man, not Duke's, whom Paul had to save David from on the hospital roof.
The Crooked Man isn't actually Duke's ghost
This is actually heavily implied by some of Paul's dialogue and several in-game documents. It's implied that The Crooked Man is some sort of pre-existing malevolent spirit that "imprinted" on Duke and later David, taking on elements of the former's appearance and personality due to his influence on it. The vision of David's mother in the hospital basement was likely the Crooked Man itself, or another spirit like it, taking on the form that would be most likely to drive David to suicide. Note that Paul and David, even when they know about the previous tenant and what happened to him, consistently describe the Crooked Man as if it's a separate entity or manifestation, not to mention the book in the hotel that describes entities that sound suspiciously like the Crooked Man, and the documents covering a patient who killed themselves to escape something sounding suspiciously like the Crooked Man... which then is implied to have gone after his doctor.
The Crooked Man is actually David's subconscious self-loathing
Just a thought that David didn't really get over all of his failures in life and wants to punish himself for being, what he considers such a pathetic existence. Thus he developed a DID and his other personality took the form of the Crooked Man who is after him.
The game uses "The Sixth Sense" ghost logic
None of the ghosts seem to know they're dead, similar to the movie. It's possible when D says he's taken the bar exam five times, he's only actually taken it once in life, which is why he's failed the others. A majority of the ghosts in "The Sixth Sense" didn't realize they were dead, and would do the stuff they did in life. (Like maybe taking a bar exam?)
Shirley didn't leave David of her own will
Ties in with
The Sandman (2014).
In The Sand Man bonus ending, we are treated to a few tidbits of information. The orbs that The Sand Man extracts from humans are parts of their soul. We also learn that different humans have a combination of different colored orbs inside of them, and that, at one point, The Sand Man took a pink orb from a human and then returned it. How does this relate to Shirley? Well, it is implied in The Sand Man that Sophie's insomnia stems from her insecurities related not only to her friends and family, but her feelings for David. When she extracts the pink orb, she can get to sleep, and Sand Man keeps the orb for safekeeping in the happy ends so she can finally sleep. The other fairies discuss and infer that Sophie is "too young" for her jewel to be returned. So if the jewels are emotions, then that means that Sophie inadvertently extracted her love into the jewel, and Sand Man is holding onto it because they feel she's too young to be tormented by her feelings for David.
Now, who else do we know in this series who seems to have lost their feeling of love all of a sudden, with no real explanation? Shirley. Maybe Sand Man extracted Shirley's romantic feelings at some point in her relationship with David, and without the ability to feel love she gave up on the relationship and left him. But, by the end of the game, she's suddenly in love with him again and wants to be with him, even though nothing major has changed in their relationship premise; he's still somewhat of a doormat, and it's clear that she doesn't want to be with him just out of pity that his mother died. So maybe after the Sand Man extracted her love, he witnessed the consequences of his actions and decided to return Shirley's love to her, and that's why she kept trying to reach out to David and reestablish her relationship with him. It wasn't that she wanted to break up with him at all, she just suddenly lost her love for him and that led her to make the decision. When they get back together, she seems very confused about her feelings at the time, almost as if she's trying to find a way to rationalize a decision she made back when she had lost her feelings.
