Talking about single-funded payment channels, the idea is quite simple: Alice puts 10 btc into a multi-sig signed with Bob, and then they each update the state accordingly to send money to each-other back and forth.
Now, imagine a third person joins the picture, say Carol. And Alice wants to send her some btc. Can the channel state be updated with someone else's public key?
I'd like to understand if something like this is possible. If not, I'd like to know why this isn't possible (I'm for sure missing something about how payment-channels work and I'd like to understand what). Perhaps using Channel Factories something like this is possible?
The main idea here is that someone can set funds aside for a new person, without having to create a new channel, but by using the funds in an already created channel.
Please note that this doesn't have to do anything with routing. It's simply using funds within a channel for another person rather than just the 2 parties of the channel.
Perhaps there's the possibility of creating "off-chain channels" (maybe this is channel factories?) that are somewhat connected to the main branch, using other participants. I want to stress that in this example Carol has never participated in a on-chain channel -- she's a new participant involved using "off-chain channels":