Hi,
I assume that you are currently a member of A-kasse, and also that you meet the requirements for being eligible for Unemployment benefits (“dagpenge”).
And since you have a permanent resident visa, you seem to meet all conditions.
If you also, while receiving dagpenge, do what you have to do, this means applying for jobs, come to meetings in A-kasse/Jobcenter etc., then you will receive dagpenge fully legally, and therefor you can never be asked to pay anything back to the Danish State or the A-kasse.
You can compare A-kasse membership with other insurances you buy. You pay some fee for some time, and you may use the insurance or not, but in case you need to use the insurance, then you will get paid, but you do not have to pay back later.
You can post a comment if you need further information.
Best regards,
Anders Weber, A-kasser.dk