Although inverting companies are colloquially said to "change" their domicile to a foreign country, technically inversion usually involves creating a new parent company that sits "on top" of the corporate structure and is incorporated in the desired foreign jurisdiction.
Earnings stripping is a commonly used technique in United States domestic tax avoidance in which a U.S. corporation uses loans between different divisions of the same company to shift profits out of high-tax jurisdictions and into lower-tax ones.