The SOL for a written contract in CA is 4 years from the date of last activity, which would be whenever you last paid on the account. This would not count if they already have a judgment against you or if it is a government debt. A judgment in CA is good for 10 years and renewable for 10 and government debts have no SOL.
This does not have anything to do with the length of time it can be on your credit reports, a judgment will be on there for the length of the judgment and any other debt can only be on there for 7 and a half years.
This also does not mean they cannot file a suit against you, it just means that when you respond to the suit you have an affirmative defense to have it dismissed as being time barred.
This will also not stop them from wanting their money. They do have the right to try and collect by calling you, sending you letters and etc. forever, you will always owe the money even if there is no judgment and it isn't on your CRs.