Yes it is possible in principle: they could still serve historyless wallets, in trustless or trusted mode. The node would only provide UTXOs to the wallet, and SPV proofs for transactions that created the UTXOs.
Whitepaper Pruning
The Bitcoin whitepaper described the architecture in “7. Reclaiming Disk Space”.
Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without breaking the block’s hash, transactions are hashed in a Merkle Tree [7][2][5], with only the root included in the block’s hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored.
Reclaiming disk space
A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore’s Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.
A node that would do this would keep:
- Header chain
- UTXO state
- Source transactions of each current UTXO
- Merkle tree nodes needed to be able to construct Merkle proofs for UTXOs
Such node could still trustlessly serve historyless SPV wallets, with the caveat that they can lie by omission (hiding UTXOs that exist), or lie about spent status (server provides an existing spent TXO and claims it is unspent).
Bitcoin Core Pruning
The above was never implemented in Satoshi-era Bitcoin node, or later Bitcoin Core nodes. Instead, pruning is done by simply deleting whole old blocks, and keeping only the header chain and UTXO state.
Such nodes can validate transactions locally but do not serve as backends for light wallets: they lack both Merkle proofs and UTXO indexing by address. UTXO indexing could be added, but without SPV proof generation, this would be a trusted architecture: the server could fabricate non-existent UTXOs (which the client would only discover when attempting to spend) or misrepresent their content.
