I suspect they are only required to notify the court that employment has terminated.
The employer must notify the court of an employee's termination and file a motion for release.
Although there were some changes to the garnishment laws in Michigan a few years ago, the employer/garnishee can be held liable for the employee/debtor's entire debt if the employer screws up and fails to get a release from the order.
The garnishment order, in other words, remains in effect and is binding on the employer until notice from the court (or issuer).
The employer also must provide the employee's last known address and the name and address of the employee's new employer (if known).
Litigator's post contains inaccuracies and is not reflective of Michigan laws.