Hello, I was on limited contract which has expired...

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It is different whether your contract is fixed-term or unfixed
If your contract is fixed-term, you cannot terminate it unless after the expiration of the contract term
If your contract is unfixed, you must notify your employer before the terminating the contract, depending on the period you have spent with the employer. The UAE Labor Law stipulates that:
Article 113
An employment contract shall terminate in any of the following cases:
By mutual agreement of the Parties, provided that the worker's consent is given in writing;
Upon expiry of its term, unless it has been expressly or implicitly extended according to the provisions of this Law;
For the convenience of either party to an indefinite term contract, provided that the provisions of this Law concerning the notice and the valid grounds of termination without arbitrariness are adhered to.
Article 116
Where a contract is revoked by the worker for reasons other than those specified in
Article (121), he shall be required to compensate the employer for any damage the latter sustains as a result, provided that the amount of compensation shall not exceed half a month wage for three months or for the remaining period of the contract, whichever is shorter, unless otherwise stipulated in the contract
Article 117
Either the employer or the worker may terminate an indefinite term contract for a valid reason at any time following its conclusion, by giving the other party a notice in writing at least 30 days prior to termination.
For the daily-paid workers, the notice period shall be as follows:
One week: if the worker has been employed for more than six months but less than one year.
Two weeks: if the worker has been employed for not less than one
year.
One month: if the worker has been employed for not less than five
years.
According to the given facts and for clarification purposes, we would like to explain to you,
According to the federal labor law in regards of resigning from work without the consent of the employer, it is the two cases
 Article (118)
The contract shall remain valid during the notification period referred to in the preceded article and shall terminate on its expiry. The worker is entitled to his full wage for this period based on the last wage, and he should work during this period if the employer requires so.
The parties may not agree on the exemption of the notification condition or to reduce its period, however they may increase this period. 
Article 121
A worker may leave work without notice in one of the following cases:
1-    If the employer violates his obligations before the worker in the articles stipulated in the contract or the law.
2-    If the employer or his legal representative signs an assault on the worker.
Article 128
A non-National worker, who abandons his work without a valid reason before the expiry of his definite term contract, may not, even with the employer's consent, take up other employment until the lapse of one year from the date on which he abandons his work. No other employer may knowingly recruit such worker or keep him in his service before the lapse of such period.
Article 129
A non-National, who notifies the employer of his desire to terminate his indefinite term contract but abandons his work before the expiry of the statutory period of notice, may not, even with the employer's consent, take up other employment until the lapse of one year from the date on which he abandons his work. No other employer may knowingly recruit such worker or keep him in his service before the lapse of such period.

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We would like to inform you that you will receive the end of service bonus, and you will receive the expenses of your return to your country. You must leave immediately upon the end of your residence visa or search for another job before the end of the visa to transfer your sponsorship to the new work. As long as the contract is of limited type, there is no notice period, as the notice period is in the unlimited contract according to the Labor Law.

Here are the texts of the articles relating to your inquiry according to the Federal Labor Law:

Article (131)

Upon expiry of contract, the employer shall bear the cost of the worker’s repatriation to his point of hire or to any other point that was mutually agreed upon. Where a worker joins another employer upon expiry of his contract, the latter shall bear the cost of the worker's repatriation at the end of his service.

Without prejudice to the foregoing, if the employer fails to return the worker or to pay his repatriation expenses, the competent authorities shall do so at the employer's expense and may then recover any expenditure incurred in this connection by attachment. Where the reason for the termination of the contract is attributable to the worker, his repatriation shall be at his own expense if he has the means to pay.

Article (132)

 A worker who has completed one or more years of continuous service shall be entitled to severance pay at the end of his employment. The days of absence from work without pay shall not be included in calculating the period of service. The severance pay shall be calculated as follows: 1. 21 days' wage for each of the first five years of service. 2. 30 days’ wage for each additional year of service provided always that the aggregate amount of severance pay should not exceed two year's wage.

Article (133)

A worker shall be entitled to severance pay for any fraction of a year he actually served, provided that he has completed one year of continuous service.

Article 137
Where a worker under an indefinite term contract abandons his work at his own initiative after a continuous service of not less than one year and not more than three years, he shall be entitled to one-third of the severance pay provided for in the preceding article. Such a worker shall be entitled to two thirds of the said severance pay if his continuous service exceeds three years up to five years, and to the full severance pay if it exceeds five years.
Article 138
Where a worker under a definite term contract abandons his employment at his own initiative before the expiry of his contract period, he shall not be entitled to severance pay unless his continuous period of service exceeds five years.
Article 139
The worker shall be deprived of his end of service gratuity in the following two cases:
a - Should he be dismissed from service for any of the reasons set forth in Article 120 hereof or should he leave his employment in view of avoiding the dismissal there from in accordance with the said Article.
b - Should he leave his employment of his own accord , and without notice in cases other than the ones set forth in Article 121 hereof , and such with regards to contracts with undetermined term , or prior to the completion of five years of continuous service with regards to contracts with determined term
Note that the employer cannot take any legal measures against you
Because you did not commit any mistake punishable by law