Students that receive Pell Grants should be required to pay back a percentage of the money received if they are expelled from their education program due to unethical academic behavior, such as cheating or plagiarism.
American education is by itself a big incentive for foreign students. They may not mind, if they could afford, to be paying their way through schooling in the USA.
Otherwise create loans for them like all Americans kids already need to get, so as to encourage and retain brilliant students from other countries.
Kids who graduate early still receive benefits until 18. Kids how are delayed receive until 19 and 2 months. By adjusting the limit to the sooner of secondary graduation or attainment of age 18, we could save millions.