Do you mean that the "signature chain" can prevent double spending?
Can a "signature chain" prevent a 51% attack? I doubt it?
'Signature chain' without blockchain can't. Satoshi and the others (above post) found that out.
But in our 'signature chain' project we have the 'transfer signatures' plus 'transfer transactions' that are timestamped on the blockchain. So we can know which signature was first, so it works. Satoshi didn't have a blockchain to do this, he had to create one what we use.