How often do independent franchisees typically survive the demise of the franchisor?

It’s been in the news lately that there is only one Blockbuster Video left in the world now.

I know Showbiz merged with Chuck E. Cheese’s decades ago, but two years ago I ran across a Showbiz Pizza still operating in the mountains of Virginia. It still had a fully functional Rock-afire Explosion band.

What typically happens to franchisees when the franchisor fails or does something the franchisee does not like? How can they keep using the franchise name?