Soft Forks are changes in crypto asset protocols that follow the new system, but also still follow the previous system, as long as they do not violate the rules of the new protocol.
The soft fork event only requires that most of the miners need to update the system and use the new rules. This is in contrast to a hard fork which requires all nodes to upgrade and agree to a new version. This type of fork only requires most miners to upgrade to enforce the new rules, as opposed to a hard fork which requires all nodes to upgrade and approve the new version.
Miners who do not update can still see that the new incoming transaction is valid. However, when a miner does not update the system and tries to mine a new block, the block will be rejected by the network.
This is because the soft fork is represented as a gradual network upgrade mechanism, in which miners who want to update the system will be given incentives, and if not, most likely, the miners will experience a decrease in functionality. One example of a Bitcoin soft fork is SegWit and non-SegWit, where both of these software use the Bitcoin network.