In some countries they then wind up the targets of investigation and receive tax bills and fines.
... and other corporations notice that, and locate their new facilities someplace more welcoming.
I don't think your comment supports dropping the corporate tax rate to zero, but rather better policing and tax law management.
Every dollar the government spends on better policing and better tax law management is one dollar less for something else. Likewise with every dollar that corporations spend on tax avoidance. US corporations already spend about $200 billion per year on tax avoidance. If the corporate income tax was cut to zero, all of that money could go into something productive, and the end result would be higher overall tax revenues from payroll taxes, sales taxes, excise taxes etc.
I've seen the claim that corporate income taxes inhibit job creation, but I've not seen convincing evidence that it does.
When a company moves its headquarters overseas, the executive and administrative jobs go with it. When American businesses spend hundreds of billions on accountants and tax attorneys, that is just dead end spending that results in no useful goods or services, and no job growth.