The company can't sign a labor contract with retired Aunt Wang. When workers reach retirement age, the relationship between them is not labor relationship, but labor relationship or employment relationship. Labor relations or employment relations are not regulated and protected by the Labor Contract Law, but by the civil law.

People's Republic of China (PRC) labor contract law

Article 2 This Law is applicable to enterprises, individual economic organizations, private non-enterprise units and other organizations (hereinafter referred to as employers) in People's Republic of China (PRC) to establish labor relations with laborers and conclude, perform, modify, dissolve or terminate labor contracts.

State organs, institutions, social organizations and laborers who have established labor relations with them shall conclude, perform, modify, dissolve or terminate labor contracts in accordance with this Law.