"When I last saw him he was dying, but now you'd hardly know he'd been ill"
Solution 1:
You've got it backward: CGEL is saying that for some speakers bare he was dying entails his subsequent death, because dying is a process which ends in death. These speakers insist on something like he seemed to be dying—which evokes a contrast between the "seeming" and the reality—to change the entailment into an implicature.
Here's the relevant excerpt:
The Cambridge Grammar of The English Language (Huddleston & Pullum 2002, p. 122).