That's not correct.

1st, the citizen who is sponsoring an immigrant is means tested.

2nd, UCIS must use their judgment to determine the immigrant has the means to support themselves and won't become a public charge.

This applies for all immigrants applying for permanent residency.

Also I'm not just talking about relatives sponsored by lawful immigrants, I'm also talking about relatives sponsored by citizens.

Btw unless a permanent resident is sponsoring their minor child, sponsoring another immigrant is generally a multi decade process.

Even the spouses of green card holders aren't considered immediate family and the average wait time when sponsoring is over a decade.

The sponsoring immigrant is means tested on their behalf.

At some point those people will be responsible for themselves and the sponsor's responsibility expires.

Only after the person either becomes a US citizen or has done 10 years of qualifying work.