People with antibodies could even temporarily earn more than others, since they'd be able to work without restrictions.
> poorer people trying to get the disease
Rich people like money too, so it would be most working people.
I'd be more interested in the percent of the population who continue to be carriers. What do you do with them? Lock them up for life?
While that's trivially true rich people like money less than poor people -- simply because of diminishing returns. If I hand a homeless person $100 they'll be a lot happier with that than if I hand Bill Gates or Jeff Bezos $100.
If we do allow people with antibodies to work then for a poor person getting the virus might save them from starvation or homelessness or any one of a thousand terrible things that happen if you run out of money. If you have even the smallest amount of money saved up on the other hand it's not really worth risking your life since you won't end up malnourished or on the street in either case.
Presumably people without symptoms still develop antibodies, I don't think there will be any Typhoid Marys.