If you are not paid salary for the last two months, your contract with your employer is terminated automatically.

I came to the UAE in May 2016 on an employment visa with a cleaning service company. There was another man with me. My partner got his Emirates ID issued after three months, but till date I have not received mine. When I asked my employer regarding the same, he told me the company would take care of it and that I needn't worry. Moreover, for last two months, we haven't had many customers and have not received our salaries, either. Our boss has now told us we can look for a job outside if we want. I asked him about my status, but he refused to talk to me. What should I do? Am I living in the UAE illegally? Should I go to the labour court or police station to file a complaint?
Pursuant to your queries, we assume that your residence visa is not stamped on your passport considering the fact that you have not yet received your Emirates ID. It is the responsibility of the employer in the UAE to make necessary arrangements to get its employees' visa stamped on the passport upon completion of medical examination by the health authority and upon applying for UAE Resident ID (obtaining biometrics of the employee) with the Emirates Identity Authority. The stamping of employment visa on the employee's passport should be processed within 60 days of entry to the UAE on employment visa. Since you arrived on an employment visa, you are entitled to receive salary from your employer.
Since you are not paid salary for the last two months, your contract with your employer is terminated automatically if you file a complaint with Ministry of Human Resources and Emiratisation. This is in accordance with Article 2 of the Ministerial Decree No. 765 of 2015 on Rules and Conditions for the Termination of Employment Relations. It states: "An employment relation is considered to have de facto ended if any of the following instances occurs:
1. It is duly established that the employer has failed to meet contractual or legal obligations to the employee (as in, but not limited to, the non-payment of salary for a period exceeding 60 days)
2. The employee has filed a court complaint against an employer who failed to secure employment of the employee as a result of the shutting down of the employer's business, in which case a report by Labour Inspection attesting to the fact that the business has been inactive for a period exceeding two months must be obtained and the employee must have reported to the ministry during this period.
3. A labour complaint is referred to the court by the ministry and a final ruling is obtained in favour of the employee stating that the employee is entitled to not less than two months' wages or to indemnification for arbitrary firing or early termination of a fixed term contract, or any other benefits denied to him by the employer for no lawful reason or the including the end of service benefit."
If your residence visa is not stamped on the passport, your employer should be liable to the authorities. Pursuant to the aforesaid, you are advised to approach the Ministry of Human Resources and Emiratisation and file a complaint. 
Source- http://www.khaleejtimes.com/legalview/salary-default-for-two-months-voids-contract