In “Zayd came and Amr left,” waw simply joins two occurrences. In the legal illustration, however, payment is the requested act and freedom is the legal consequence. Their contextual relation permits a circumstantial reading.
Primary sense: joining two items.
Contextual, figurative sense: making freedom dependent on payment.
Legal consequence in the illustration: freedom is not established before the payment condition is fulfilled.
This does not mean every waw creates a condition. The expression, context and subject must support the secondary reading.