Yes "risk" does take an article. "risk" is a countable noun. So your sentence becomes, "These workers do not expose themselves to the* financial risks* of losing a job, as they become an asset for their employers."

"These workers do not expose themselves to the financial risk of losing their jobs, as they become an asset for their employers." - Using "the" does not make sense unless a specific, definite financial risk has been previously introduced to the reader, listener, or as here specified "the risk of losing their jobs". "These workers do not expose themselves to a financial risk, as they become an asset for their employers." (I removed the specific risk) There may be a risk. There may not be a risk. "These workers do not expose themselves to financial risk, as they become an asset for their employers." "risk" in general. No article. The confusion perhaps is that "risk" can be used as either countable or non-countable. You can certainly take risks. Riding motorbikes or skateboards or skydiving. You can also take on risk (in general). Get into debt near your means to pay.

If you are not sure if something is countable or uncountable do not look it up in a dictionary or try to google it. It will only add to your confusion as many nouns can be either, depending on how they are used. Instead think to yourself 'Can there be two of this thing?' In this instance there can be more than one risk, so in your sentence risk is countable. However, as you are referring to a particular risk, use the definite article

In my opinion, it's not that you can't use an article with "risk", but that you used the wrong article. You could say, "THE financial risk" not "A financial risk." I'm American, and that's how I would say it. It is however, sometimes correct to say "a risk": EXAMPLES" I am taking a risk hiring someone inexperienced, but I think she will do a good job. I took a big risk buying such an old car, but so far I haven't had any problems with it. Buying stocks is always a risk, but the potential payoff is worth it. Sometimes "risk" is a countable noun, and sometimes it isn't. It depends on the context. Hope this helps!