What seems to be happening in the case of failing free schools in Sweden is that:
schools have folded leaving students without a school half-way through their final year
local schools have suddenly found themselves having to find room for students of failed schools, despite not having the space or the resources
I have all my family and many of my friends in Sweden and I can't find anyone who has a good word to say for the new educational model. And the local press haven't been too enthused either.
It has increased social division without doing a thing for improving results. In fact, Sweden, which used to be top of international league tables has now slipped down, whereas Finland, which retained the traditional system, is still on top.
Some of the main problems do seem to have been with Muslim schools who have used the less rigorous inspections to introduce systems of gender discrimination (excluding menstruating girls from lessons) and types of discipline (corporal punishment) which are not actually legal. A bad example was Römosseskolan, Gothenburg; as reported in the local press, its closure last year did put a lot of pressure on the other schools in the city.
Having said this, of course there is no guarantee that the same things would happen here. It would depend very much on the inspection system.
The Swedes were new to the game, they have continuous assessment rather than external exams (which lay them open to marking inflation unless teachers and headteachers are highly principled), they had virtually no previous experience of faith schools and the school inspection system has been allowed to lapse over the years.