What if we created the inverse of what a blockchain proof of work or proof of stake system does.

You would send those coins that needed to be burned to the Phoenix blockchain (atomic swap?) which can be viewed as it's an open ledger. The blockchain would create a wallet and encrypt the privkey on the blockchain. With every new block on the chain is simply another layer of encryption that would need to be decrypted.

I believe this can be done and even perhaps reversible, which would make it interesting as then it's basically a cryptographic wallet on the blockchain for all coins using the Phoenix blockchain. I'd imagine this can be done for loans for example or gambling.