What happens to the blood drained out of the body before embalming fluid is inserted?

It is not a two-step process. Fluids are pumped into the body and simultaneously blood is drained into a collection bucket. It is then flushed into the sewer system. The blood has some embalming fluid mixed in with it, and some embalmers put other chemicals into the collection bucket before flushing. This method has been demonstrated as safe, even if it sounds otherwise.