What I want to say is, that Jennifer could have maybe stayed in the basement, but not all the time. Maybe the first letters went to the real Joshua, who died then and Wendy also used Jennifer – just like Gregory – as a substitute for her gone love, adressing him with Joshua and prince.
And just like with Gregory, Jennifer accepted that out of pity and the own wish to be loved and accepted.
If that would be it, then Wendy wanted the bear as the only real connection between her and her old, lost love and as another substitute. She also got angry at Brown (doll or not), because she noticed that her beloved Joshua was leaving her alone again (this time not by dying, but being unfaithful to her love by loving someone/something else).
That could also be a reason, why she came up with stray dog, trying to make Jennifer so scared that she would return to her position as Joshua after the plan with killing Brown/destroying the Brown doll hadn’t worked.

A lot of what you have missed (that is, the documents) will be found in the first 4 articles placed in the “Important Resources” section.

Denise wrote:

But, in the process of becoming Joshua, Wendy split her persona. On one side, she was the shy, timid and sickly Wendy, while on the other side she was the evil, cute, and manipulating Joshua. which is why in the beginning of the game you see Wendy and Joshua hand in hand, forehead to forehead, etc.

There is a drawing made by Wendy, put up on the wall of the sickroom, which shows her hand in hand with Joshua and which might represent a dual personality.

But in the forehead-to-forehead encounter with Wendy in the pre-game video, the person that says that she is “Joshua” is Jennifer.

If Jennifer loved the teddy bear, that might be a major reason for Wendy to ask for it. By swapping the broach for the teddy bear Wendy succeeded in removing a rival for Jennifer’s affections from Jennifer’s life (as Wendy would later want to do with Brown as well), while at the same time getting Jennifer to wear a token of their love.

I interpret it more as Wendy wanting something that reminds her of Jennifer. Sort of a substitute for when Jennifer isn’t around. And it means more to Wendy because it possibly means a lot to Jennifer (like you mentioned, she would’ve become attached to it during her stay with Gregory).
Not only that, but it did belong to Joshua to begin with, so it has duel meaning for Wendy.
(for the record I don’t really support the evil Wendy theory I think she acts the way a love starved orphan might act in order to keep what little love they have )

So I was wondering if Joshua the Bear had seemed, possibly, important to Jennifer, or if Wendy was the only one the Bear mattered to.

Imagine a little girl kept in pretty much solitary confinement for 9 months with only a teddy bear for company. Do you think that the teddy bear would become a companion to her and come to mean a lot to her?

If Jennifer loved the teddy bear, that might be a major reason for Wendy to ask for it. By swapping the broach for the teddy bear Wendy succeeded in removing a rival for Jennifer’s affections from Jennifer’s life (as Wendy would later want to do with Brown as well), while at the same time getting Jennifer to wear a token of their love.

I don’t see Jen taking it as a token of acceptance quite like I read Revenant Child say. It seems that the trading of gifts is a personal thing, not about the orphaange or Gregory. They say their promise as they do it. At least for Jennifer it seems to be. Which was why I was unsure why she brought the bear with her.

But Wendy’s brooch seems to be important as well. It’s like “I want you to have this, that way you’ll always have a peice of me with you.” It kinda makes the blow harder when she flings it across the floor. So I was wondering if Joshua the Bear had seemed, possibly, important to Jennifer, or if Wendy was the only one the Bear mattered to.

I also thought of somehting else.

What if Jen actually asked Wendy for her brooch?

In the little princess chapter, the story book has the Princess Doll in it. There was a debate going on that this “Rose Princess Doll” may have been jennifer’s doll at one point. What if Wendy got the brooch off the doll? Or the brooch just reminded Jennifer of the doll and she wanted it? Wendy may have used Jen’s asking to get the Bear.

“Bring me the bear. Then I’ll let you have it.”

Maybe?