you can only subscribe as a new member in A-kasse, if you stay in Denmark at the time you apply for membership.
If you already are member of A-kasse, you can keep membership in the danish A-kasse, if you are going to work in a non-EU country, and the country does not have unemployment Insurance.
But be aware that in case you can keep your membership, and later will be unemployed, you can only receive unemployment benefits (“dagpenge”) from a danish A-kasse if you move back to Denmark, and will be available for the danish labor market.
Let me know if you have further questions.
Anders Weber, A-kasser.dk