There is an idea called the law of one price.
Assume they're making a durable, easily transported grain. Rice, maybe. Assume this is the only thing made in the entire world, because life is complicated and this abstract example is supposed to be simple. Call the local currency J's (because it's easy to reach on my keyboard).
Finally, assume rice is \$2/lb in the real world, 10J/lb locally.
Presumably, some rice-buying speculators should be willing to offer about \$2 to get 10J, roughly.
But, to make things more complicated, there are other practical questions:
- How reliable is the supply chain to get rice from this country? What is the risk?
- How about transportation costs? Rice rots, eventually, must be shipped dry, etc.
- Are there other uses for J? When other goods are introduced, how do we deal with the fact that this direct average no longer is clear?
The comments are correct that in practice small countries tend to absorb the currency of larger countries, usually USD but even BTC has been used. The logistics of managing a stable currency are too difficult and require institutional strength and a great deal of reputation. Few investors are interested in buying into something that that might go up in smoke.