Is nirodha (cessation of suffering) dependent on the existence of suffering?
Although nirodha is usually translated "cessation", its main meaning is "restraint", "prevention" - e.g. of crime or any undesired activity/outcome. In modern Hindi, nirodh is even used as a word for condom.

If you really think about it, this makes sense. The way cessation of dukkha is achieved is through non-attachment - i.e. non-creation of conditions that make arising of dukkha possible. In other words, non-attachment is prevention of dukkha.

Prevention of X does not depend on existence of X.