It all really depends on the jurisdiction.
In most common law jurisdictions, the "nominee" is a legally existing term. The sheer fact that they are merely obfuscating another person is understood and foreseen, normally in Company Management / Trust Services / Company Administration laws. As such, their responsibility will be capped by contractual agreement with you and they can shun away, you can't.
In civil law jurisdictions, those titled as Directors or Managers can generally not relieve themselves of any personal liability, though they too can contractually hold you to compensate all the negative consequences of following your instructions.
Those legally representing the company are allowed to engage it in regard to third parties, breach of trust in regard to you notwithstanding. So if they ever have their pet koala kidnapped and they need to come up with a ransom, there is nothing stopping them from, in the moment, engaging the company's accounts, pledging some sorts of company property etc. It could even be corporate actions you learn about years later. It could take years in court (as well as tens, if not hundreds of thousands of dollars) to rectify foul play, with no guarantee of satisfactory outcome.
You should check whether the agent offering you nominee services is legally allowed to arrange them in the agent's jurisdiction. If it's a specified type of regulated action and your agent is not licensed to do it, run away. If he is, then he can't shun away from his
due diligence requirements in offering a poorly-reputed nominee to you and could be held co-responsible for bad actions in some scenarios. If it's a non-regulated service (rarely so), the agent could pretend it's a non-professional introduction.
Also, it takes a certain kind of character to be a "cheap" nominee and it attracts a certain kind of clientelle. One
Panama-papers-like leak, and you could find your company tied to a network of tax dodgers, money launderers or worse by proxy of sharing the same nominee chap. Good luck finding a real bank to onboard you after that.
So yeah, nominees - sometimes good. But probably best for very specific functions or SPVs, not as obfuscation means in a real ongoing business...