We have 2 system for the unemployed. One run by the government for those away from the job market, they other issues than just unemployment. The second is run by the unions and private contractors and is insurance based you have to when employed and meet certain criteria.
The first is under the law “loven om aktiv beskæftigelsesindsats” I can’t find a good English description or translation. If you google the text in the quotations you can find the law text in Danish. This is a form of basic universal income but you are required to participate in meeting and activities that the government tells you to. On another note these people are often used as cheap labour both in government and privately run institutions and business’.
The second is govern by the “A(rbejdsløsheds)-kasseloven” and is 22.000 pages. An English translation would be something like Unemployment check. The rules are administrated by private companies and labour unions.
Hopefully this was helpful, if not I will try again.