I met a lot of Filipinos in Denmark who has lived in this country for more than 30 years but they did not change their citizenship. They refused to give up or renounce their Filipino citizenship because of many reasons. One couple who are active in the church told me that they can not afford to lie because they are always still Filipinos. Having a foreign passport will be a disadvantage to former Filipinos who plans to own properties in the Philippines. According to the provisions of the Philippine Republic Act 8179 only 1000 square meters of urban land or 1 hectares of rural land are allowed.
Finally foreign nationals can acquire Danish citizenship without renouncing their citizenship effective September 1, 2015. It also allows former Danish citizens who lost to reacquire their citizenship. Please read the following link for more details on multiple nationality.