It is Chapter Seven that you need to refer to in answering this question which features the conversation between Dorian and Sibyl after her disastrous performance and also the end of their relationship. The answer also relates explicity to one of the central conflicts or relationships that run through the entire novel: the relationship between art and real life. Sibyl, in a very moving piece of dialogue, talks about how her love for Dorian has changed her ideas and concepts about art and life. Note what she tells him:

I believed in everything. The common people who acted with me seemed to me to be godlike. The painted scenes were my world. Iknew nothing but shadows, and I thought them real. You came--oh, my beautiful love!--and you freed my soul from prison. You taught me what reality really is. Tonight, for the first time in my life, I saw through the hollowness, the sham, the silliness of the empty pageant in which I had always played.

Thus we can see that before Dorian entered her life, Sibyl's art was her reality. It was this that ironically made her attractive to Dorian in the first place, as he makes clear straight after Sibyl's speech:

I loved you because you were marvellous, because you had genius and intellect, because you realised the dreams of great poets and gave shape and substance to the shadows of art. You have thrown it all away. You are shallow and stupid.

Through her love for Dorian, Sibyl has exchanged art for reality, and as a result is now no longer able to act. Dorian, it is shown, clearly prizes art above reality, and therefore now can no longer Sibyl now she has become Sibyl, a real person, rather than just an actress who has no concrete identity.