In the case of Bitcoin, for example,...we find an invalid public key. All valid public keys begin with 0x04 if uncompressed and 0x02 or 0x03 if compressed. A pubkey beginning with any other value is undefined and thus there is no possible signature that can be created to satisfy that key requirement. Since spending coins requires signing the transaction with the correct private key, an address which has no known private key is unspendable. By using a public key which is known to not have a private key others can confirm that no private key exists.
the invalid public key we start with to generate a valid address that has no private key:
0x00000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000
Produce a valid (but unspendable) address from your invalid public key.
The Bitcoin network... any altcoin network... only verifies that an address is in the right form, length, and has the right checksum when "validating it".
The resulting pubkeyhash and encoded address will be seen as valid by the network and client but it requires a provably impossible private key to spend funds sent to that address.
The vanityburn addresses are just as useful for burn since the whole system is predicated on the fact it'd take an eternity to get a private key from a public address.. and a vanity address that is obviously not generated and noone has the private key.. is fine.. but it can have a key.. no one will know it. An address from an invalid public hash can't have any private key.