Years ago, in 2015, someone created a list of such BTC burn addresses he was aware of in this post. This other end of 2017 external site includes a longer list, and indicates that 1111111111111111111114oLvT2 was identified as Blockstore’s burn address.

When I looked at this matter recently, I focused more on 1CounterpartyXXXXXXXXXXXXXXXUWLpVr, which is XCP cryptocurrency’s proof of burn address, and I believe is the largest holder of its nature. The story behind this case is interesting, and well worth a read to understand why they burned those BTCs.

In terms of how these addresses are created, I found the following two posts to be rather clarifying:
https://bitcointalk.org/index.php?topic=5123840.msg50282766#msg50282766
https://bitcointalk.org/index.php?topic=5278431.msg55270386#msg55270386

As depicted in the above posts, these type of addresses are created to fit the structure and rules of a public address without being originated from a private key. They is therefore nobody that can actually access the burnt BTCs.

I do have the doubt though of how one can distinguish a vanity address from a burn address, whereby the former will be in control of somebody as (theoretically) opposed to the latter (perhaps the length of the legible part of the public address is part of the answer, but it seems like a simple non-exhaustive criteria).