Answer
Management is responsible for assessing the entity's ability to continue as a going concern and for preparing the statements on the appropriate basis, including any required disclosures. The auditor's responsibility (ISA 570) is to obtain sufficient evidence about, and conclude on, the appropriateness of management's use of the going concern basis and whether a material uncertainty exists.
Real-world example Management prepares a cash-flow forecast supporting going concern; the auditor evaluates it and concludes on its appropriateness.