I'll try to explain. In the beginning there were no Bitcoin addresses. You could "Pay to IP" (but anyone could claim those) and "Pay to Public Key" but those are long and ugly (an uncompressed public key is 65-bytes!) So Pay to Public Key Hash P2PKH was invented.
P2PKH takes the locking script, which may just be the public key needed to spend. Hashes it with sha256. Hashes it again with ripemd160. And then base58 encodes it (which removes lookalike characters etc). And then has a simple checksum on the end. This gave nice short addresses which humans can verify. And the checksum gave protection against mistyping or pasting a truncated address.
Since the beginning people have been abusing that base58 encode. I think 1111111111111111111114oLvT2 was the first burn address. Using an all zero hash160 result. But other famous burn addresses include 1CounterpartyXXXXXXXXXXXXXXXUWLpVr and 1ChancecoinXXXXXXXXXXXXXXXXXZELUFD. You just write 1 followed by any valid base58 characters and calculate the checksum on the end.
I expect an all zero hash160 is impossible. But for the others like 1CounterParty its likely a private key is probably possible. It will not be found until a quantum computer can reverse the hash160, reverse the sha256 and reverse public key to private key.
I'll try to explain. In the beginning there were no Bitcoin addresses. You could "Pay to IP" (but anyone could claim those) and "Pay to Public Key" but those are long and ugly (an uncompressed public key is 65-bytes!) So Pay to Public Key Hash P2PKH was invented.
P2PKH takes the locking script, which may just be the public key needed to spend. Hashes it with sha256. Hashes it again with ripemd160. And then base58 encodes it (which removes lookalike characters etc). And then has a simple checksum on the end. This gave nice short addresses which humans can verify. And the checksum gave protection against mistyping or pasting a truncated address.
Since the beginning people have been abusing that base58 encode. I think 1111111111111111111114oLvT2 was the first burn address. Using an all zero hash160 result. But other famous burn addresses include 1CounterpartyXXXXXXXXXXXXXXXUWLpVr and 1ChancecoinXXXXXXXXXXXXXXXXXZELUFD. You just write 1 followed by any valid base58 characters and calculate the checksum on the end.
I expect an all zero hash160 is impossible. But for the others like 1CounterParty its likely a private key is probably possible. It will not be found until a quantum computer can reverse the hash160, reverse the sha256 and reverse public key to private key.
There is a better explanation here: https://bitcoin.stackexchange.com/a/1852