Owners usually require a payment bond together with a performance bond. Public projects commonly require one because liens against public property are usually not allowed.
For a subcontractor or supplier, the general contractor's payment bond is protection. If the general contractor does not pay, there may be a claim against the bond.
Check the front-end documents to see if the project has a payment bond. Ask for a copy when you sign the subcontract. Bond claims have strict notice rules and deadlines that differ by state and by project type. This is general information, not legal advice. Check the bid documents and your state.