That's exactly Gresham's law. When people consider a currency to embody lasting value, they tend to hold on to it. Currency considered of doubtful value (including counterfeit), will be passed on like a hot potato.

This was particularly applicable in the days of gold and silver coin, where the weight of precious metal mattered. In colonial America, shillings were little appreciated because they were often clipped to reduce the weight of silver. The "good" money people tried to get paid in and to hoard was the Spanish silver piece of eight, or dollar. Hence...