This changed in 2012 and actually it’s one of the few possibilities the current government keeps with the new laws. But there are criterias, you should have stayed six months in DK + corporate with the police if you are rejected - and first of all it’s a very bureaucratic process to have a work place accepted. Because of this very few people actually get a job within the formal system. Getting a job outside the formal labour market is possible but the informal labour market is precarious.
Access to basic education and health care is limited. Some language tuition is accessible at the camp, but only as long as your case is treated. Children are enrolled in school or kindergarden at the camp or in the local community.
As an asylum seeker you are obliged to carry an identity card and stay, where the Migration Service decides while your case is treated. Your identity card will have your fingerprint on it. Life as an asylum seeker in Denmark is often centered around the camp and access to society is depended on social relations outside the camp. Recently many local civil society initiatives have started, establishing cafees, support with school homework, social events etc. as a meeting point between people in the asylum process and people living permanently in Denmark. Look at the contact list and ask around to find out what is going on in your area.
Living as undocumented in Denmark
People witout papers living outside the formal system depend on migrant communities and social networks. For undocumented migrants there is no access to education and only access to immediate healthcare. There are health clinics for undocumented migrants in Copenhagen and Århus. These are run by the Red Cross, The Danish refugee council and the Danish Medical Association.
The adresses and opening hours is only available if you contact the clinic privately. You can find contact information on https://www.rodekors.dk/det-goer-vi/sundhedsklinik (in Danish though). The health clinics have access to a group of voluntary interpreters.
Police controls occur randomly.