When a support function is found to be more profitable than the primary business
The Aerobie Sports company mostly makes odd-ball equipment for having a catch. But they made a coffee maker called the Aeropress as a side project and now it makes up more than half of their sales. 

The Woolworth Company (of five and dime fame) founded the Foot Locker shoe store as a side business and now it is the core-surviving brand of that corporation when the main Woolworth business was closed. 

Post it notes were a side business for 3M but now amount to \$1 billion in sales a year. But that's only about 3 percent of revenue. 

The Michelin Guide books were developed to help promote the sale of tires through encouraging road touring. It survives today and though the business might be a small fraction of the revenue produced by the tire business it has significant cultural influence and an independent life.