It depends on a lot of things, such as how much particular items are worth, and how much those that follow realise what they are worth, or value them for their own sake.
As someone else said, most of it probably ends up on the market in some way. Silent key sales at hamfests, general auctions, house clearers, ebay. Even if it's taken to the dump, the tip rats are always on the lookout for something they can rescue and sell.
I've heard of large collections of model trains disappearing. It's been suspected that the wife hated them and had them destroyed, even though they were worth tens of thousands.
Leave bequests or directions in your will, including the likely value and how to go about selling it, or giving it away. I know someone who's scaled down his collection of junk and only cautiously acquires more, because he doesn't want to saddle his brother with a silent key sale.