How is it checked that you're eligible? Asking because the system in the Netherlands could be defrauded, people registering to be living in the country, registering X amount of children, then going back to live in a cheaper country. Not sure if their children were actually real either.
(this was a relatively isolated incident but as these things go, they overreacted, set up software that over-eagerly identified families as defrauding the system and taking their benefits away, causing widespread chaos and a still-running compensation program that's costing the government years tens of billions to set right (https://en.wikipedia.org/wiki/Dutch_childcare_benefits_scand...)).
If the child are registered with the tax authority and have a personnummer (ID number) then the parents get it at their tax-authority registered bank account.
About that kind of fraud I never heard anything like that in Sweden, but I would assume social services checks if children are attending school and if they are not, they investigate the parents. So this kind of fraud shouldn't be possible long-term. Social services would get called if a child doesn't show up for school or is not registered in any schools pretty quickly.
I also think that home-schooling is illegal, but not sure on the specifics.
(this was a relatively isolated incident but as these things go, they overreacted, set up software that over-eagerly identified families as defrauding the system and taking their benefits away, causing widespread chaos and a still-running compensation program that's costing the government years tens of billions to set right (https://en.wikipedia.org/wiki/Dutch_childcare_benefits_scand...)).