[Used Can]

Well, I think that can be explained by saying that, whoever Beatrice's "host" is had them spare Battler. She seems to be the owner of the gold, and based on what we saw on EP4, she also seems to manage a fuck-ton of money. So, whoever it is working with her or having her do these things, may have complied to the request from her to spare Battler. This was quite likely agreed before October 4th, since "Beatrice" must have written those letters before that day. So, she could already tell Battler would survive until the end. There's also the possibility she committed all the crimes herself, and allowed Battler to survive until the end.

As a result, since he was the detective in the two stories she wrote, the ones who made the forgeries may have followed this pattern as well. At the very least, until EP4, Hachijō did.