Depends how much money I was offered. If my website is good enough to be bought out, odds are I update it regularly. And if I update it regularly, odds are it’s one of my main pass-times. And if it’s one of my main pass-times, odds are I enjoy maintaining it. How much would you charge if you were to sell your favourite game if you knew you could never buy a new copy?
And if I were to sell it, I’d probably make relatively identical (the archives and design would have to be different, but still the same idea) website and let the people know that that’s where I’m going. For example, if I was Kirupa, I’d sell Kirupa.com and make somethings like FlashKirupa.com where you can find convenient tutorials for Flash 4, 5, MX, Dreamweaver, etc. and I’d continue it as though I’d never stopped working on Kirupa.com.