On August 11, 2016, the first official Kingdom Hearts concert was held in Japan, called Kingdom Hearts Concert -First Breath-. Fans who attended the event were treated to orchestrated music from the Kingdom Hearts series. Voice actors for Terra and Namine (Ryōtarō Okiayu & Iku Nakahara, repsectively) were in attendance. Tetsuya Nomura, director of the Kingdom Hearts series, said "something was in the works" about a week before the concert concerning the voice actors. Something indeed was in the works!
Exclusive back story, which will not be included in-game for Kingdom Hearts 0.2 Birth by Sleep -A Fragmentary Passage-, was reenacted by Terra and Namine's voice actors, exclusively for attendees at Kingdom Hearts Concert -First Breath-. This contains heavy spoilers, so read below at your own risk.
Thanks goes to @aibo_ac7 for providing information concerning the exclusive back story, @r_kane1 for providing a summary of the information, and Kayla Copeland (email@example.com) for translating the full dialogue.
1st: Okiayu (Terra) and Nakahara (Namine) reenact some KH scenes.
2nd: Okiayu (Terra) voiced his lines as Lingering Will. Namine (Nakahara) meets some kind of darkness and speaks to it.
Namine talks about her arrival at Lingering Will. She had known about the confrontation between Terra and Xehanort. Namine and Lingering Will's conversation goes something like this (not exact wording):
LW: This is...
Namine: This is the world of your memories. In this point of time, you've forgotten where you belong, and you've followed the memories of those you're connected to and came here.
LW: Who...are you?
N: It's nice to meet you. I'm Na-- ...a witch who can control memories.
LW: A witch...?
Namine: Right now, you are caught between two memories. One is your very own memory. The other is that of a very great darkness.
LW: Master... Xehanort...
Namine: Soon you will touch a familiar light. She will guide you so that you do not get lost in the darkness.
LW: She... Aqua! But, I can't do anything as I am now...
Namine: Everyone is fighting now in whatever way that they can. You too, you must believe in yourself, that you will not be lost in the darkness, and fight. Because the place everyone will arrive to is the same...
LW: Aqua... Ven... Someday, I will absolutely...
("The Unknown" is playing)
LW: I haven't forgotten a thing from that day. I'll get there, without fail.
Through this conversation with Namine, Lingering Will remembers Aqua and Ven.
Nomura then revealed that this is a story that takes place shortly before 0.2. He also said that this conversation between Lingering Will and Namine is a treat for concert-goers today, and it won't appear in the game.
UPDATE: This conversation is transcribed inside of the official Kingdom Hearts Orchestra - World Tour - guide. It has both the Japanese conversation, and the conversation translated to English. It turns out this conversation was not between Lingering Will and Naminé, but it was actually between Terra and Naminé. View the conversation below with the official English translations thanks to @jsjunshen:
Naminé: Don't worry. You might forget about me . . . but with our promise I can come back. Yes. One day the light--it will be ours, and it will bring us together. And then--I'll be in your heart.
Sora: Right. Forgotten--but not lost.
Lingering Will: Aqua . . . . Ven . . . .
A Keyblade? Who are you?
I know you. We've met before, way back when. No, that wasn't you. You're not the one I chose. Where is he? Xe . . .ha . . .nort . . . . Is that you? Xeha . . . nort . . . . Xehanort!
Lingering Will: That's it. your Power
That's what I felt within you.
The power that conects to Aqua.
And to Ven's heart.
Terra: Where am I . . . ?
Naminé: In your memories. Traces of you were lost, so I found you through memories belonging to those you've met in the past.
Terra: Who are you?
Naminé: I'm Naminé. It's nice to meet you.
I'm a witch who can control peoples' memories.
Terra: A witch?
Naminé: Right now you're bound to two memories. One belongs to you, the other belongs to an unspeakable darkness--
Terra: . . . Master Xehanort.
Naminé: Your heart will soon encounter a familiar light. You must make sure she isn't lost to the darkness. You must guide her.
Terra: Her? You mean Aqua? I'm not sure what I can do to help, not like this.
Naminé: You must fight, Terra, like the others. You mustn't let your heart melt into darkness; follow your true memories, and you'll reach the light. She's headed there, too--to the same place. You must believe in promise, just as she continues to believe in you.
Terra: Aqua. Ven. One day I'll--I've never forgotten our promise. Never. I will keep fighting.