Back in the good ole days; currency was valued on commodities versus today where our money's value comes from fiat. In other words money was valuable because it was made from precious metals (gold and silver). While today money has value because governments say it does.

So money would just continue to circulate until it naturally phased out due to wear or reuse. Sometimes it was collected and melted down to form new coinage. Other times it was melted to form jewelry or other materials.

Further money still retained its value due to what it was made of. Hence why merchants in those times carried scales to weigh money in order to insure it was equal to what it was represented to be. As many people made their living devaluing money (chipping away at the gold for example).

Many Roman era treasure horses were found to contain coins from many different eras of Roman rule. Meanwhile Viking hordes often contained coinage from all over the world; interestingly enough a lot from the Far East and Muslim areas in particular.

Basically money would naturally die off as there was little need to replace it.