Can a foreign employee claim to have signed an open-ended labor contract with a company?

Depends on the region. In practice, some courts, such as those in Shanghai, Sichuan and Hainan, have held that the terms of an open-ended employment contract between two parties are invalid on the basis of the provisions of the Regulations on the Administration of Foreigners' Employment in China, which stipulate that the term of an employment contract for foreigners shall not exceed a maximum of five years as a peremptory norm. At the same time, some courts, such as the Beijing and Nanjing courts, in accordance with Article 14 of the Labor Contract Law of the People's Republic of China, found that the employer and the worker had entered into an open-ended labor contract.