There are three exit paths, and each is one transaction from the creator.
Withdraw
Withdraw moves value out of the vault to any address: vault.withdraw(to, amount) for the native currency and vault.withdrawToken(quote, to, amount) for anything else. The bursar keeps running, and the vault keeps receiving the fee stream.
Stop
Stop operator sets the operator to zero, halting the bursar: vault.setOperator(0x0). Claims are permissionless, so anyone can still claim on the token’s behalf; proceeds go to the vault either way.
Hand back
Hand back points the fee stream at any address you choose, after which the vault receives nothing further: vault.handBack(newRecipient). It is irreversible from our side.
None of these requires anyone at Bursar, and none of them needs this site to be up.

