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We would like to inform you that if your inquiry relates to the submission of your resignation, which your employer has approved, the following information are important :
The Qatari Labor Law has granted the employer the right to receive compensation from the worker upon the illegal termination of the definite employment contract.
It is the judge who estimates ​​the compensation.
Also, if the worker fails to provide a notice for the employer of his desire to terminate the indefinite employment contract, a compensation shall be paid to the employer equivalent to the wage of the worker for the duration of the notice period.
There is no legal provision obliging the worker to bear the cost of cancelling the Qatari ID card.
Here is the text of the Qatari Labor Law related to your inquiry:
Article (49)
If the service contract is of an indefinite duration any of the two parties thereto may terminate it without giving the reasons for the termination. In this case the party intending to terminate the contract shall notify the other party in writing as follows:
1. In respect of the workers who receive their wages annually or monthly, the notification shall be given not less than one month prior to the date of the termination if the period of service is five years or less. If the period of service is more than five years, the notification period shall be at least two months prior to the date of termination.
2. In all other cases the notification shall be given in accordance with the following periods:
A) If the period of service is less than one year the notification period shall be at least one week.
B) If the period of service is more than one year and less than five years the notification period shall be at least two weeks.
C) If the service period is more than five years the notification period shall be at least one month. If the contract is terminated without observing these periods, the party terminating the contract shall be obligated to compensate the other party for an amount equivalent to the wage for the notice period or the remaining part thereof.

You may file a complaint at both the General Directorate of Passports and the Human Rights Department against the employer for the cancellation of residence and ID card.