You tell you have not been member of a Union…do you mean an A-kasse (Unemployment insurance Fund)?
In Denmark membership of A-kasse and Union are two different things.
Only membership of A-kasse can give you right to Unemployment benefits.
However I assume that you haven’t been member of either an A-kasse nor Union.
In this case there is not possibilty to have Unemployment benefits in case of unemployment.
In Denmark Unemployment Insurance is voluntary, and therefor only people who buy the Insurance (A-kasse membership) are insured againt unemployment.
However if you will continue to live in Denmark after termination of your employment, there will be the possibilty that you can
get the lower social allowance called “kontanthjælp”. However this is only possible if you dont have money/savings yourself.
But about kontanthjælp you must contact the municipality where you live.
We only guide about A-kasse and Unemployment benefits (“dagpenge”), not kontanthjælp.
Anders Weber, http://www.a-kasser.dk