If billionaires stopped spending what would the economic effect be? For example they always invest every available wealth they have (or they burn money for cooking or dump money into the sea to make artificial islands)?

In some sense that money is not returned to the economic system.

In other words what are the effects besides the money supply decreasing?

I am asking this to satisfy my curiosity.
If one person decides to reduce his lifetime consumption by (say) \$100, then someone else (or many someone else's) is made richer by \$100.  For example, that $100 might be left to a single heir.  Or at the other extreme, the person might decide to burn a \$100 bill in which case the benefits are spread to everyone who holds money.  

When people are richer, they can decide to consume more, or to work less, or some of each.  Because income elasticities of labor supply are empirically quite small, you'd expect most of this to come out in increased consumption.