MissTriggs, yes, that phrase could be used too.
But race to the bottom can also describe a broader situation, with multiple parties. So eg a UK clothing company may ask manufacturers in the Philippines, India and China which can offer it the best deal. The companies compete to offer lower prices, by cutting wages, cutting H&S, using unsafe buildings, etc. Plus the UK company suggests local government offers it a deal to win the business - lower taxes for five years, exemption from local pollution laws, etc.
Eventually, one company wins the work. But the workers don't earn enough to pay the rent they need to live near the factory, and are injured by the work. And the local area doesn't receive much income and suffers the pollution.
So the contract wasn't really worth winning.
Race to the bottom describes this whole process. Once you recognise it, you can watch variations of this in operation everywhere.