Yes there are naturalized citizens with many kids on welfare BUT
the government bringing in more lazy immigrants with many kids is not helping anyone.
Statistics actually show that immigrants, both low-skill and high-skill, are usually highly productive and provide major economic benefits, especially in the long run. "Lazy" is just a far-right buzzword in this context. Here's
a nice report on the matter.
Even if some immigrants do indeed cost more than they bring in, they are hugely outnumbered by the beneficial ones and there's no point to introducing a selection process which is bound to unintentionally also refuse so many "good" ones that the potential economic benefits suffer.
Also it's kinda cynical to say that bringing in immigrants who end up on welfare is not helping anyone. Obviously it does help those on the welfare which, if you have the slightest bit of compassion, is a good thing. And if you lack that compassion, well, it's still a small price compared to the economic benefits provided by the other immigrants.
Also, if immigrants can be stuck on welfare "forever", as sambo12345 put it, that's a universal problem that affects all families on welfare, immigrants or not. Even oh-so productive and disciplined Germany has or at least had big problems with Germans preferring to live on welfare over getting a job.