It's also likely you inherit the connections your parents make - provided you maintain a good relationship with them. Everyone once in a while, I'll heard about a guy by mum knows who needs some work done on his website. Since my mum is an assistant in Tesco, these are not stupendous opportunities (though not to discredit, I can use the money).

If my mum or dad was an investment banker and I was still a web developer, I imagine they would still send leads my way. There just may be more in quantity or monetary value or both.