As opposed to all other forms of social security in Denmark, unemployment insurance is voluntary. This means you are not automatically insured against unemployment when working in Denmark.
If you want to be insured against unemployment while working in Denmark, you have to join a Danish unemployment insurance fund, also known as an "A-kasse". This means that being entitled to unemployment benefits is dependent on a membership to an A-kasse.
The unemployment funds are private associations which, in most cases, are associated with trade unions and other professional organisations. It is however not mandatory to be a member of a trade union in order to become a member of an unemployment insurance fund / A-kasse.
You can become a member of an unemployment insurance fund if you are at least 18 years of age, still have 2 years left before you reach your old age pension age and reside in Denmark (or another EU/EEA country and work in Denmark).
For more information on unemployment insurance in Denmark, how to claim unemployment benefits, special rules for cross border workers and much more please visit lifeindenmark.dk.