The earlier discussion of faṣl and waṣl asked whether two distinct judgments should be coordinated. In circumstantial predication, the structure is different: one clause gives the main event and another supplies an attendant state. Linking pronouns and wāw are therefore analysed with reference to the bearer of that state.
The final test is semantic: is the later clause a new independent assertion or a circumstance qualifying the preceding event? That distinction determines which set of rules applies. The exact form of a verbal circumstantial clause must still be tested against its tense, polarity and the intended relation to the bearer.