When asked about the ending scene, which is still arousing viewers’ interpretations, the director said, “As I said, I wanted to present the relationship between Doona and Won-joon, which is like a fantasy, in a realistic way. Who knows how life will go? No matter where they are now, how they live, or whether they may meet each other again or not, they will always remember the other in their lives.” 

I mean he said it ladies and gentlemen, open ending! 

People will hate me for saying the following, spoiler alerts.

It was really weird how he acted when she came to see him after she returned to stage.  An idol made her escape to see him, he should have been very happy, but his responses were cold and calm.  Over the series he's been kind to her, it's out of his character to hurt her like that.  He knows she's lonely and she even said you are abandoning / discard me and he said yes.  Unless it's bad writing, otherwise, there maybe a deeper reason.

And here is the sinister opinion.  He mentioned he is very poor and with a sick sister and it's around that time Doona was forced back to stage.  There were few scenes, first one he told his mom do what is needed referring to his sister's treatment, also he saw his mom sleeping outside hospital room tired, as well as running on street feeling ashamed and frustrated.  I wondered if he received some money from the company after they saw him kept texting her showing how he missed her.  They may have investigate and reach out to him and offer some money to help with his sister's operation.  He may eventually accepted.  This may explained why he was cold toward her, since he has an agreement with the company to stay away from her.  Years later when she has more control of her career, he should be able to be with her, but he still shows coldness.  Until she confronted him in his apartment, he finally told her, he did her wrong.  She gave him that chance to apologize since she did the same before. 

I do believe they made up afterward as some mentioned that opening scene where they met up at different scenes.   However, due to the agreement w/ the company they can only meet up in secret.  That also explain at the end, when she walks down the hall hearing his voice she wasn't surprised that he's also in Japan, as they will meet up later.  He's also smiling thinking to buy a cake for their meeting later.

Of course, maybe it wasn't the money, maybe it was that he just feel so ashamed that he's powerless to help her.  

PS I think couple reasons he let go other than contract issue is also because he knows she loves singing and another is because he felt they are in 2 different universes.

That’s the thing I don’t disagree with many orwith you ,  to me it seem they reconciled. I agree except when they say is not a open ending, the Director left it a open ending so we all interpreted it how ever we want. He said it we don’t know where they are or if they meet again or not.  So what we say is allegedly or wishful thinking.  As a avid reader, PA and writer myself I can say is not fair to discard the opinion of the creator. There are the only ones that can say yes this happen or not. I talked to some one and I told that person well the director said this and she said I don’t care is this and that. Well she lives in a delusion, the only one who can say on what happens to a character is of those who create them.

The 'open ending' has only been done successfully with a very few directors. This isn't one. The great open ending isn't. It will appear to be but will have very subtle clues that make observant viewers go 'oh!' There are no open ending in real life. Most 'open endings' are lazy or are there purely to play mind games.

There are open endings in life though. Wrong place, wrong time happens to many people and sometimes it leaves a lingering bittersweet feeling. I think the open ending here encapsulates that perfectly.