You cant say come here illegally and live with me to anyone you feel like - you would get 10 years inside for people trafficking. You can’t just have an underage kid arrive illegally in the country and move into your house - it breaks just about every law there is. Pimping, child abuse you name it.
Before you get near a benefit you need passport/birth certificate, proof of residency and a dozen other tests.
No evidence the benefit claims go up 50,000 a year. No evidence of illegal migrants getting benefits. How hard is this to understand?