Is it true that whatever is subject to cessation is subject to origination? Dhamma implies that whatever is subject to origination is subject to cessation. 


  And while this discourse was being spoken, there arose in that bhikkhu
  the dust-free, stainless vision of the Dhamma: “Whatever is subject to
  origination is all subject to cessation.”


But what about the opposite?

Is it also true that whatever is subject to cessation is also subject to origination?
Buddha said:


  yaṃ kiñci samudayadhammaṃ, sabbaṃ taṃ nirodhadhamman'ti 


or "whatever is samudaya-able -- all that is nirodha-able".

Samudaya means "to come together", "to arise from coincidence of multiple conditions".
Nirodha means "to stop".

So the meaning of the phrase is "Whatever arose from coincidence of multiple conditions will stop when one of those necessary conditions is no longer operative."

You're asking, what about the opposite? Can something that has stopped like that - can it arise when the necessary conditions come together again?

The answer is, yes of course it can - but is that new "something" the same as the original "something"? In Buddhist understanding, this answer depends on clinging and identification. If we cling to it and identify with it as the same - then for us it is the same. If we don't cling and don't identify - then it's not.

The next question you ask: if suffering comes from coincidence of multiple conditions, and one of those conditions is craving, if that craving is removed, the suffering stops - but can the suffering arise again? Yes, of course it can - if all the necessary factors, including craving, come together again.

Why would craving happen again? Craving happens when we think that object of craving is desirable. Why do we think that object of craving is desirable? Because we think that getting that object will lead to good experience for us. Why do we think that getting that object will lead to good experience? Because we think that good experience comes from the object, not from ourselves. Why do we think that good experience comes from the object? Because we don't understand how our mind creates experience. This is called "ignorance".

So if there is still this "ignorance" => there will be craving => there will be suffering.

Nirvana is permanent cessation of suffering attained with complete cessation of ignorance (of how mind creates experience).