Tom Homan has suggested that Rep. Alexandria Ocasio-Cortez could be under investigation related to immigration issues, but there is no verified evidence that she employed an illegal immigrant on her congressional staff or that such an individual fled the country.
Tom Homan confirms an investigation is underway into Rep. AOC for employing an illegal immigrant on her congressional staff — the individual has since fled the country.

FactVerify
Source: factverify.com
What the Evidence Shows
The claim states that Tom Homan confirmed an investigation is underway into Rep. AOC for employing an illegal immigrant on her congressional staff and that the individual has fled the country. The search results show that Tom Homan, a former ICE official and border czar, has publicly suggested or floated the possibility of investigations into AOC related to immigration matters, including allegations of impeding immigration law or hosting events aiding illegal immigrants.
However, none of the credible sources confirm a formal federal investigation specifically about AOC employing an illegal immigrant on her staff. Furthermore, there is no evidence in the search results that any such staff member existed or fled the country. The sources mostly reflect Homan's statements or opinions rather than official DOJ confirmations or investigative findings.
Therefore, while there is some discussion about potential investigations or calls for them, the specific claim about employing an illegal immigrant and that person fleeing is unsubstantiated and misleading based on available information.