In March 2016, the Migration Court stopped all forced returns of asylum seekers from Sweden to Hungary under the Dublin regulations. But in July, the higher Migration Court has decided to allow returns to Hungary again.
The family that was treated in the case could stay in Sweden, however, as they have two small children and as there was a big risk that the family would have to stay in a deportation center in Hungary for a long time.
This means that in general, asylum seekers that have finger prints in Hungary will be returned there. But it means also that it could be worth to appeal against deportation decision, especially if small children are involved. We recommend you to get in touch with a local asylum group or a lawyer to receive legal assistance.