Can non-qualifying people claim beneifts?

When applying for something like a UK visit visa - or just entering for 6 months without a visa - is the wonder whether the applicant has enough funds to cover their travel period.

My question is can those without status in the UK claim benefits? If they can, I understand UK immigration rules' case. If they can't, why does it matter if they don't have enough money? One of the main aspects of applying for a UK visa is the uncertainty if an applicant will rely on public funds. But if the applicant was ineligible to do so, why does it matter? Or can anybody just claim UK benefits?

Thanks. So confused!

Not just anybody can claim benefits, especially not a visitor visa holder.