In emerging markets, it's not uncommon for transactions be split between a portion that's reported to the tax authorities and an unreported cash transaction. So, if a counter-party suggests this, how should you respond? One approach is to act oblivious and continue as though you didn't hear them. Because it's illegal, they'll likely hesitate to recommend it explicitly if they don't know you.
But, if they persist and try to explain how they want the transaction to proceed, you should tell them that that's unacceptable. If their response makes you feel uncomfortable, walk away. There are plenty of profitable transactions that won't expose you to FCPA risk.
While this form of corruption may be more prevalent in emerging markets, unfortunately it exists everywhere. It's just a matter of degree. So, know your values and be sure to live by them.