You still can in Argentina and Paraguay.
Paraguay up until recently required a ~5k deposit but they dropped even that. In Argentina "technically" you're supposed to follow a bunch of rather restrictive resident visa pathways but few do that and you can file for citizenship immediately upon landing and until your case is finished cannot be deported. The requirements are basically live there for 2 years and show you had some income, but by judge shopping some allow black market income lol.
Others of note: Bolivia and Somaliland only require a token payment for a 1 year resident visa (think in Bolivia you only need do that 2 or 3 times to become PR or citizen). If you have a bit more cash several places like honduras / nicoragua / ecuador only require ~30k "investment" which is basically accessible (eventually) to anyone middle class+ with enough determination. When I went to Rojava they also accept basically anyone as they are a "people without a nation" who happen to have sort of a nation.
And then there's weev, who posts here on occasion. I think he got a Transnistria passport, which is obtainable after only a year of residence. It's my understanding residency is as easy as going to a hotel and asking to talk to the right people about getting a resident permit, and paying some moderate fees.
If you're not too discriminating pretty much anyone can emigrate from the US forever with very little capital.