That seems extraordinarily unfair to the developing countries, especially if it becomes something that people do en masse.
Trust me, they're not going to end up paying for anything old retired westerners need.
E.g. It's nearly impossible to emigrate to India as a retiree, unless you can obtain OCI/PIO status.
This isn't true of course, unless you're referring to the tiny amount given to asylum seekers?
If you think it is true, name the country and the specific benefits available to people with no residence and no visa.