you dont write in your inquiry whether you are a EU/EEA citizen or not, and what type of residence permit you hold. Thats important in relation to Unemployment benefits.
To be eligible for Unemployment benefits your residence permit must give you the right to stay beyond your job PhD-contract.
For EU/EEA citizens:
If you are an EU/EEA citizen there is no problem - you can stay in Denmark and in relation to Unemployment benefits you will be treated like a danish citizen.
As an EU/EEA PhD-student you have two options to become a member of and receive benefits from an a-kasse.
You can become member of an a-kasse like other salaried persons. You must pay the normal member fee, and you must fulfill the requirements. But one of the requirements is that you must have been member for at least 1 year before you apply for benefits. In your case this will not be possible. At the moment you are only member of an Union (IDA). Memberhip of an Trade Union does not give you any right to receive Unemployment benefits. To being eligible for benefits you must be member of an A-kasse.
- Your option would be to sign up with an a-kasse as a graduate and take advantage of the special favourable requirements for being eligible for benefits. You will receive a little less in benefits than with the option 1, but the requirements are easier to meet. You can see our guide for graduates here: https://a-kasser.dk/graduates/.
For non EU/EEA citizens:
As a non EU/EEA PhD student you are not allowed to receive unemployment benefits during the job search period of your residence and work permit.
However, as a foreign national who has completed a Danish PhD degree you can apply for a residence permit with the aim of establishing yourself in Denmark (an establishment card). If you have received a residence permit under the establishment card scheme, you can legally stay in Denmark and can accept offers of employment with one day's notice. Therefore, it will be relevant for establishment cardholders to apply for membership of an a-kasse.
How to become member of an A-kasse? If it, according to the above, is relevant for you to become member of an A-kasse, this is easy to do, because everything is online, and the only thing you should do is to fill out a online form on the website of the A-kasse you decide to be member of. You can see our guide on "How to apply" here: https://a-kasser.dk/member.html
Hope this helps you.
Best regards, Anders, www.a-kasser.dk