An unpermissioned ledger is an older name for what is now usually called a permissionless blockchain, where the design, examples and trade-offs are covered in full. This page explains the term and why both names exist.
A ledger is unpermissioned when no gatekeeper decides who may take part. Anyone can download the software, keep a copy of the record, submit transactions and, by following the network's consensus mechanism, help decide which transactions are added. Bitcoin and Ethereum are the standard examples. The opposite is a permissioned ledger, where an operator or consortium approves participants, as is common in bank and supply-chain projects.
The phrase "unpermissioned ledger" was common in early reports on distributed ledgers, including work by central banks and consultancies around 2015 and 2016, when writers were sorting the new systems into categories. Over time the industry settled on "permissionless" as the usual word, and "public" is often used alongside it, although the two are not identical: a ledger can be public to read yet still restrict who may validate.
The trade-off is the same under either name. Open participation brings censorship resistance and neutrality, but it needs costly security measures, such as mining or staking, because participants cannot be vetted in advance.