The pension fund (CalPers) is a non-profit completely independent of the State Budget.
Yes there's $1 trillion in unfunded pension liabilities.
The reason they can have a $10 billion budget surplus at the same time is that the way government accounting works, the only pension expense is whatever they actually contribute to the pension funds in a particular year. If for example they contribute nothing, then no expense! Unlike corporate pension plans which have an expense regardless of what's contributed.