The No-Pay, No-Play Rule prohibits uninsured drivers from collecting non-economic damages from at-fault or negligent drivers. Even if the uninsured driver is injured, they won't be able to recover such damages from the negligent party. However, if the party responsible for the accident is uninsured, they may still be liable for economic and non-economic losses.
This rule tries to encourage drivers to get insurance and comply with their financial responsibilities to the state of California.