A lot of parents with non-Danish origin are sending their children out of Denmark so they can attend boarding schools with strict structures so the function like behavior modification facilities.
The Danish parliament has passed a law several years ago which removes the grants given to parents in Denmark who have children aged 17 or less.
If you as parent fail to report that your child has left Denmark and continue to receive these grants, it is embezzlement. You will be charged with a criminal offense.
It is rather complicated to report that your child has left Denmark and you risk an investigation by the social services because Denmark is fighting general foreign behavior modification. Some parents have already been jailed for two years because they have sent their children out of Denmark.
You can avoid all that by not allowing your child to become an exchange student.
Taken into consideration that accreditation of foreign education is imposssible because Denmark in general has curriculum of too high standards, your child cannot benefit from such a stay abroad. Choose a short term language school lasting 1-3 weeks instead if the goal is to become informed about foreign culture and language.
Children abroad used in welfare fraud, Denmarks Radio, June 17, 2010