when you receive supplerende dagpenge, you must be available for the labour market, like it you were on "normal" dagpenge. This means that you must accept job offers from the Jobcenter.
Offers from the Jobcenter must as far as possible be based on yours wishes and assumptions for permanent employment. But the start of point is that you must accept the offers from the Jobcenter, if you are not able to find something your self.
As long as you don't accept reasonable job offers from the Jobcenter, you will not receive dagpenge.
If the Jobcenter finds that you do not have the necessary ability or will to be available, then it can have severe consequences for you, because you can lose the right to receive dagpenge. If that happens you must work 300 hours before you can get dagpenge again.
Anders Weber, www.a-kasser.dk