I didn't do much research on the topic, but from what I read a peg-out can only be initiated by a member of the Liquid federation. You are right about that part. When you initiate a peg-out, an equal amount of L-BTC has to be burned from the Federation's supply. When that is done, your requested funds will be sent to the address you previously whitelisted.
You can read a little bit about it here >
https://help.blockstream.com/hc/en-us/articles/900001408623-How-does-Liquid-Bitcoin-L-BTC-work-I've heard about this in the past, but had no idea that the peg-in requires 102 confirmations before you get credited with your L-BTC!