They didn’t physically “lose” their visa like they might lose their car keys; they OVERSTAYED their visa. It doesn’t matter how the person originally arrived. It only matters what their present residency status is.
In all the foreign countries our family ĺived, we entered legally and had a work/residency visa w a defined duration. At the expiration of that visa, we didn’t expect the host country to pay to enroll our kids in college.