Children attending school in Sweden who are not fluent in Swedish must receive auxiliary Swedish lessons for as many years as are necessary. The same children may receive (but it is not compulsory) special instruction in their home language, not only when they are preschoolers at home, but continuing on as they, their parents, and the school authorities feel it is necessary.
For example, a Dutch family moves to Sweden, where the father intends to work for the next several years. The parents have a 3- year-old, a 10-year-old, and a student in the upper secondary school.
The family wants the preschooler to become fluent in Dutch, to learn the same Dutch grammar and composition and vocabulary as a child preparing for a Dutch school. And the older two children need help in Swedish to be able to keep up in their school classes.
At the same time, the parents don't want the older children to lose their Dutch, or to miss developing a better understanding of Dutch prose and poetry while in Sweden.
It is incumbent on the Swedish municipal authorities to fulfill these language needs, and as often as possible, classes of Dutch/Swedish children are formed so that the work of one teacher can be used by many children and not a just a handful.
And while the primary effort of the schools is for fluency in Swedish (in order to understand school lessons), there is, according to Swedish authorities, an almost equal commitment to developing and maintaining the home language. This includes study lessons not only for the children, but for the adults in the home as well.
Of course, Danish and Finnish are two of the home languages most frequently spoken by immigrant children, and often there are enough preschoolers in a single language group to make up a special class with bilingual teachers. But efforts in Sweden are to break up these groups as soon as possible in order to hasten the children's understanding and use of Swedish for school instruction.