Even if the idea that is formulated is for a business that the employer isn't in, and left a decade ago (servers for data centers)? Or if the main idea is "I want to do my next chip design for someone else"? Doubtful.
Doesn't matter IIRC, most employers requires their employees to sign an agreement saying that anything they come up with during the term of their employment is owned by the employer unless the employer gives up rights explicitly. This is to prevent someone from getting "The next big thing" then running away to start a company for it even though their employer was interested.