We know that Willoughby expected to find Marianne dead or nearly dead by the time he got there. He decided to make his 'apology' to Elinor only after he found out that was not going to happen.

So, if he thought Marianne would be dead or about to die, why did he come? The death of a character like Marianne, after being horribly used, publically humiliated and cast aside by someone like Willoughby would be what would be expected in the literature at that time.

We have some clues at what Willoughby really intended. Ch. 44 is full of references to Willoughby's vanity, both by himself and in Elinor's thoughts. Willoughby admits more than once that Marianne's behaviour towards him elevated his vanity, and this 'deathbed scene' he hoped to play out was yet another example of his vanity where Marianne is concerned.

Even some of his lines sound 'scripted', like what he planned or imagine he would say. For example "Had they told me," he cried with vehemence, "that Mr. Palmer and all his relations were at the devil, it would not have turned me from the door."

For example, in the novel Clarissa, which Jane Austen certainly read, and which featured a heroine who died after being seduced by the villain Lovelace, this same Lovelace writes, following her death "Let me know, if the d——d mother be yet the subject of the devil’s own vengeance—if the old wretch be dead or alive? Some exemplary mischief I must yet do. My revenge shall sweep away that devil, and all my opposers of the cruel Harlowe family, from the face of the earth."

Here, he tells Elinor he was envisioning this deathbed scene as he travelled to Cleveland:

"I had seen Marianne's sweet face as white as death. That was the last, last look I ever had of her; -- the last manner in which she appeared to me. It was a horrid sight! Yet when I thought of her to-day as really dying, it was a kind of comfort to me to imagine that I knew exactly how she would appear to those who saw her last in this world. She was before me, constantly before me, as I travelled, in the same look and hue."

And this is the part that shows that Willoughby, in his vanity, really thought that Marianne's final thoughts in this world would be of him, that she would literally die with him on her mind:

"What I felt on hearing that your sister was dying -- and dying, too, believing me the greatest villain upon earth, scorning, hating me in her latest moments -- for how could I tell what horrid projects might not have been imputed? -- One person I was sure would represent me as capable of anything. What I felt was dreadful!"

As he travelled, he had this whole scene in his head that Marianne would die or had died, thinking of him in her final thoughts and that he would sweep in and either see her there, all white as he had imagined her, or hear her in those last moments forgiving him, but still with him on her mind.