Currency is an arbitrary, made up system that exists as long as those participating within the system agree it has value.
Like Greenfield already ninja'd me on this, currencies based on actual precious metals are generally valued by their mass of that metal.
So unless the loser's currency is easily devalued by shaving, hollowing, being alloyed with base metals, or other forms of forgery, it will be valued by its equivalent mass in the victor's coin.
On occasion, coins of the defeated were outlawed, so you'd melt yours down and have it recast...unless you were a loyalist rebel, that is, and the coin was used as a symbol of resistance.