If only a minority of miners switches to the new rules, there is the risk that the blockchain ultimately forks. We end up in a situation similar to a hard fork. Miners running on the new software will only recognize blocks mined by miners who have updated and reject blocks that have been mined by miners running under the old set of rules. Since miners who have updated their software are in the minority, their chain is not the longest chain. It will therefore be disregarded by miners operating under the old set of rules which results in a permanent split of the blockchain.
Is that understanding of a soft fork correct?
Yes, that's an accurate description.
The only distinction I'd make is that it's only
permanent if the legacy chain remains the most-work (longest) chain forever. If the soft fork chain ever overtakes the legacy chain regarding accumulated work, it'll result in a chain reorganization. All of the legacy chain's history between the fork and the reorg would be lost.
This is why it's ideal to have a supermajority of miner support before activating a soft fork. It ensures backward compatibility so there is no chain split.
