I have encountered several merchants around Firewatch who by default have no gold to barter with. Here is a list of those I have encountered so far:

• Dorash gro-Drethan (Enchanter)
• Ragru gro-Ghash (trader, outside with a stall)
• Helsanni Moon-Beam (trader, outside with a stall)
• Lyanna Ismal and Ra'Meale (both inside Chatal Mendor: Fine Armorer. Possibly not a bug due to Chatal being the primary shopowner, but his gold amount is quite small, especially for being a fine armorer)
• Rajasi (trader, outside with a stall)

I tried to check as many merchants as I could after noticing the issue, so most shopkeepers seem to be fine.