The majority will leave, certainly but there will be stragglers.
Assuming sane citizenship policies, miscegenation laws, etc.; what’s to stand between a white man and colored labor save for an oppressive government? If coloreds want to work as menial/manual labor they should be deloused and inspected by the respective state to ensure they’re disease free. Coloreds are then registered and micro-chipped. They give birth on company grounds with colored midwives.

Colored children must be provided some form of vocational training by their employer. If they are injured or ill the employer is entirely responsible financially. In the event a colored commits a crime the employer is billed for the room and board along with the lethal injection if deemed necessary. When they die, they’re to be buried on company grounds. In the event of overcrowding, white cemetaries and churches retain the right of eminent domain over colored boneyards.

This may seem harsh but after BRA crumbles the choice between a miserable post-entitlement existence and a job in the South will be tempting to many coloreds.