Coinmaking came to a stop with the fall of Rome. Coins were produced again in small quantities from the 7th century onwards in some places.
In the 6th century, many Roman coins are still around. But a "bag of coins" is an abstraction. It can also be a pouch of amber or raw silver or even gold nuggets. Anything that people would in general accept as payment.
Much local trade is conducted by barter or exchange. For many everyday things, the characters can trade a hare they hunted or a tool they found or forged.
quotes (from "Money and Coinage in the Middle Ages")
The basis of the new late Roman system was the solidus, a coin weighing
(in Roman terms) 24 carats/siliquae, equivalent to 1/72 of the Roman pound
(4.54 grams) (Figure 4.1). This new coin was probably introduced in 309 in the
mint at Trier, which was then the most important of the mints controlled by
Constantine, who had established his residence in the city. It was progressive-
ly struck by the other imperial mints, replacing the heavier Diocletian aurei
(weighing 1/ 60 lb = 5.46 grams).
Although silver continued to be coined, it no longer enjoyed the importance
it had maintained under the Principate, instead playing a secondary role com-
pared to gold.
In the second half of the 5th century, the AE
4 (often referred to as the nummus) remained the only bronze denomination
struck by the imperial mints.