First of all, I believe that the notion that Mary and Laura had one final meeting is simply wishful thinking. That's unjust though right? How come she went all that way, all alone, only to come up empty handed? But did she really come up empty handed? I submit to you that even happy endings in Silent Hill are not devoid of dark spots. Next, Laura is an orphan, you might say Mary was the closest thing she had to a real mother. Mary cared for Laura, so its only natural that Laura would seek her out after getting her letter. Recall that during their time in the hospital, Mary showed Laura pictures of Silent Hill and told her about their trips. She knew it was special to Mary, so she found a way to Silent Hill to search for Mary. Throughout your journey in Silent Hill 2, you run into Laura on several different occasions. Obviously, Laura does not appear in the Abyss/Labyrinth.
It is important to mention that Silent Hill 2 is the story of James and Mary. Not James, Mary and Laura. Laura, like Angela and Eddie are merely supporting characters. However, James and Laura are connected by their common search for Mary. We know she has a particular distaste for James which only is exacerbated when she finds James killed Mary. Some believe James should have told a "lie of omission" and said she was sick and that's how she died and let Laura go on to believe that. Laura even says that herself. I believe this works against the notion Laura and Mary met one last time. Had Mary and Laura met once more she would have uncovered the real truth: that James did in fact murder Mary. This would have deepened Laura's dislike for James and would have made her less inclined to want to leave with James, much less let him adopt her. I reject the notion that Mary would have explained that it was done out of mercy. To a child, murder is wrong. Its right and wrong, black and white. When you are a child, there is no middle ground, no in between. Further solidifying its James' fault Laura can't be with Mary. Therefore, reducing the chance that Laura will trust James.
Secondly, let's assume for a moment there was a meeting. Mary appears to Laura and they have one final meeting, but Mary cannot stay with Laura. Laura has to leave once again without Mary. In her letter, Mary also states that she is in a "quiet, beautiful place." She didn't tell Laura she died. This would break Laura's heart. It also stands to reason this could create some ill-feelings toward Mary. Laura may have felt betrayed and lied to. Furthermore, it teaches Laura an important lesson by not seeing Mary once more. Mary is dead. Laura needs to learn that means Mary is not coming back and that Laura should move on with her life. She should try to be happy and not hang on to the past. She needs to learn to let go. If Mary appeared to Laura one more time, it could screw up Laura's perception of death. She needs to learn death is final. She might start to believe that anyone who dies would come back (though I realize that point is a bit of a stretch.) We also must take into account that Mary knew she was dying. She didn't know she was going to be murdered, but knew she was close to death. Mary had no intention of appearing to anyone after she died. In this respect, it is not as if Mary chose to appear only to James and purposefully left Laura out.
Perhaps the most important facet of this theory is the letter to Laura. The way I see it, the letter is Mary's final word (or meeting, if you will) to Laura. Mary mentions she would have liked to adopt Laura. I would argue that after his final talk with Mary, James feels the need to adopt Laura partly to make up for his crime. He feels the need to do something good, to forgive himself. As an adult, he probably also feels a sense of responsibility. He shouldn't leave this little girl alone in such a place. Besides, up until the point of the Lakeview Hotel, Laura still has not found Mary. She asks James if he has and if not then they should leave.
So there you are, James. Did you get the letter? Did you find Mary? If not, let's get going already.
This quote almost suggests that Laura is losing interest. Of course, this is just before James reveals he killed Mary, but I believe it changes nothing. I believe that after the final confrontation with Maria and the conversation with Mary, James catches up with Laura. I don't know exactly what happens next, a conversation of some sort ensues. Maybe he tells her the whole truth and she understands. Maybe he tells her of his final meeting with Mary. James promises to give her a good home and take care of her, because that's what Mary would have wanted for Laura. Though I don't believe James does this just because Mary would have wanted it. Mary also wanted James to go on with his life. In this act, the connection between James and Laura is completed and they can go on with their lives. Finally, it may seem unjust that the two didn't get to meet one last time. It may not seem right. However, as we learned in the SH3 OST's "Hometown" track, "this movie doesn't end the way we want all the time." It is for these reasons that I believe a final face to face meeting between Laura and Mary simply did not happen.
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EDIT (03/25/20): Cleaned up some characters.
EDIT (04/04/09): Cleaned up some aspects of the post, rewrote/removed some things for clarity.