True. What actually happens, is the opposite, known as Thier's law[0]: "Good money drives out bad". When given free choice (free competition between currencies), people prefer to accept the good money, which eventually drives out the bad money from circulation. Or more clearly, the bad money loses demand and therefore its value.

[0] https://en.wikipedia.org/wiki/Gresham%27s_law#Reverse_of_Gre...)