In the form of welfare benefits (50%+ of households)...

You're going to have to justify that number (either a link, or clarifying some details). I did some searching, and was unable to verify that. I'm sure there is fraud in the system (especially among actual citizens). But nothing like you're claiming. The closest I was able to find was that US-born children do receive benefits (since they are citizens), even with undocumented parents. If that's the number you're quoting (which was pretty close), they are US-born citizens. Doesn't count. Plus, you can't deport a citizen. Note that most welfare beneficiaries are children even in US households.

If you don't have documents, you are ineligible for welfare benefits.

Digging a bit further, they are a net-positive on the US economy. Some localities will vary because of costs of education and healthcare (ERs). But they are a net positive impact on the US, generating significant economic activity, filling labor shortages, and paying $23B in taxes in 2023. Numerous links with this information. Just picked this one at random:

econofact.org - How tighter curbs on immigration impact the u s economy.

And, to reiterate, I don't approve of the exploitive nature of this. We need to fix this. Just providing data on the realities of it.