Wow, there are a lot of things going on here so hopefully I've understood it all correctly.
By the sound of it, your client purchased the supplier then populated that supplier's website with their own content?
If this is the case, I'd expect their biggest issue will be the duplication. If they've now got 2 websites with the same content, it's very likely this alone with limit the second site's ability to rank well.
While having duplicate product descriptions isn't the end of the world, it certainly doesn't help. In this scenario they've taken unique content and replaced it with duplicate and so the drop you're seeing is exactly what I would have expected.
My question is what's the best thing to do in this case so that the rankings will be back to higher positions and they'll get back their traffic.
If I were in your shoes, I'd be looking to get as much uniqueness happening in that content as I could. Since the supplier's site had original content for the same products, you could try reverting to that for the time being. You can test it with a single category as a proof of concept and if that works, move ahead from there.
If you're going to try that, make sure you block the subdomain via Robots.txt so Google isn't crawling those old descriptions there or you'll end up in the same position
This is all general info since I can't look closer at the site. It could also be a site structure/speed/navigation/page title/meta description problem etc. If you're comfortable sending me the links I'd be happy to take a closer look. Feel free to drop it here or PM.