Hi bradif1,
If I may offer a brief suggestion, cessation means both that everything completely ceases, and that things partly cease.
A paradox? Not really! It’s just a matter of time.
When someone attains arahantship, certain of the aspects of dependent origination cease immediately, such as ignorance, craving, and grasping. Things such as rebirth in a new life also “cease” immediately, although in a somewhat different sense, because here what is meant is the potential for rebirth.
Other things, like feelings, six senses, and so on, do not cease immediately. But since the cause for them is no longer present, they will inevitably cease in the future, i.e. when the person dies.
This distinction stems from the nature of the conditions in the series. The nature of the conditional link between members of the series varies in complex ways. However they have one thing in common: they are a necessary condition.
So when the causal link is broken, the exact manner in which that manifests will vary. However, there is one thing they all have in common: when their necessary condition is gone, the thing itself will cease.
tl;dr: in dependent origination, when ignorance ceases, everything else ceases, but some things take some time.