Let's imagine a situation wherein a language has quirky case. The language normally is nom-acc, but the situations where quirky case appear are all underlyingly erg-abs.
The language has quirky subjects as well as objects. Let's for the sake of simplicity assume that subjects sometimes are dative, objects sometimes ablative. Here, any substitutions, even to the extent of replacing both with the same oblique case, could work. I am just establishing this in order to have a terminology that makes it clear.
canonical quirky subject nominative dative object accusative ablative
Now, how does the underlying ergativity look? Well, let's decide on some quirky verbs:
verb1 : 'to have the time to', 'to do on time', 'to have time for'
verb2: 'to forget (to do something)'
verb3: 'to refuse (a proposal, a guest, a gift or a favour)'
verb4: 'to fear'
Now, let's consider what the underlying ergativity of these implies: the subject of verb1 would be absolutive if there is no direct object, and thus can be coordinated with another intransitive verb:
I have time to wait and (so) (I) sit here
however, it cannot be coordinated with a transitive verb:
I have time to wait and __ (am) eating pirogies
With a direct object, however, we get the following situation:
I have time for the committee and will discuss the issue
However, an intransitive second verb will take for its subject the object of the previous verb:
I have time for the committee now and will be seated in room 101
here, it's the committee who will be seated in room 101. Semantically, this seems to be a reasonable thing - whoever has time for a thing may be seen as active in some sense, and the object may be more likely to do intransitive things.
Similar examples could be constructed for the other verbs, obviously.