Yes and No: it will run out of cash, but will be able to replenish it, and pay its claims, by asking for contributions from insurers in the state.
After the SoCal fires in 2025, the CA Fair Plan will likely run out of cash: Will California’s FAIR Plan Have Enough Cash for Its Wildfire Claims?
In order to pay its claims, it will ask for additional funds from all insurers offering policies in California: California FAIR Plan to assess insurers $1 billion for LA wildfires
In turn, these insurers will be able to recover up to half of these funds from their own policy holders (that means us), who will end up paying for some of these claims: Homeowners insurance rates to rise in California FAIR plan
In this manner, the Fair Plan remains solvent, and allows us all to keep finding insurance for our homes.