I think the key bit is "granted asylum". When people show up, they aren't granted asylum. They apply for it, and an immigration court adjudicates. So, from what we've sussed-out here, until you're granted asylum you don't get government benefits (federal...individual states may have different laws).

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I didn't know we were limiting the definition to just federal welfare. Many of the benefits come from the various states but there are certain federal benefits the seekers can get and do get.

Here is the scam being perpetrated - the Federal government allows unlimited seeking of asylum and rebukes arguments about the cost of benefits by claiming as you do "until you're granted asylum you don't get government benefits". Then the seeker goes onto the queue waiting on a hearing in 3 or 4 years. During those 3-4 years, 26 states IIRC grant state welfare benefits PLUS SCOTUS ruled years ago the children of seekers are entitled to schooling PLUS all the seekers are entitled to medical care PLUS if the female seeker gives birth while here, she, the baby and the rest of the family unit become eligible for SNAP.

Then there is the cost of housing, language training, job training etc which is often taken up by charities but then on the back end, the Federal Government provides grant money to the charities who provide these services. Same with Legal services for the seekers, many of the attorneys who provide assistance are paid in part with federal grants to Legal Aid societies.

In fairness most of these costs are not direct federal welfare but grants to NGO's who provide welfare like services is a distinction without a difference. So the scam as I call it, is just the Federal Governments way of hiding the true cost of supporting seekers while they wait.

Here is a headline,

Federal spending bill to include $800M in grants for cities dealing ...
Dec 20, 202212/20/2022 03:17 PM EST. Updated: 12/20/2022 03:34 PM EST. NEW YORK ' A federal spending bill will direct $800 million to cities like New York struggling to provide for thousands of migrants...

Here is another headline,

NY says it needs $3 billion from federal government in coming years to ...
Dec 17, 2022CNN ' New York is hoping to receive $3 billion from the federal government through 2026 to handle the influx of migrants that city leaders have been grappling with for months, according to a...

Here is one more but there are plenty more like these examples,

NYC to receive $100M from FEMA to help with asylum seekers
Jun 7, 2023New York City is poised to receive more than $100 million in new federal funding to help manage the surge of migrants, Spectrum News has learned.

It is fine to support unlimited seekers because of genuine compassion but don't think there is hardly any costs to taxpayers while the seekers wait on their hearing. And many of them when they do get their hearing will be denied asylum status so their consumption of taxpayer dollars while they waited was sort of wasteful.