Under California law, debt has a statute of limitation. The length depends on the type of debt and the creditor.
Claims for breach of written contract—which includes normal consumer debt, like credit card debt—has a four year statute of limitations. Cal. Code Civ. Proc. § 337. Debt collectors are required under California law to tell the person contacted if the statute of limitations has passed on their debt. If the account has had recurring payments, the four year time limit starts with the last payment. (Cal. Code Civ. Proc. § 337(2).)
If the debt is the result of an oral contract, such as a handshake agreement to buy something for a specific price, the statute of limitations is two years. Cal. Code Civ. Proc. § 339.
If you have debt related to property damage, such as from a property you have been renting, the limit is three years for the debt to be collected. Cal. Code Civ. Proc. § 338.
Even when the statute of limitations is up, the debt can still show up on your credit report. Unpaid debts generally stay on a credit report for seven years. 15 U.S.C. § 1681c.