Take a look at Freicoin ( http://freico.in/ ). Inactive coins are slowly flushed out. As are all others, which is probably not what you want, but it you might think it is a good idea after reading the Freicoin material.

A neat pair of advantages of Freicoin is that since all coins "rot" at the same rate, mining is always relevant even with the currency having a fixed supply cap, and also the blockchain can be pruned (i.e. it doesn't have to "grow forever" for most "full node" clients).