Final answer:
The client in this scenario is experiencing Stage 4 of illness, which is the advanced stage requiring surgical intervention.
Step-by-step explanation:
The stage of illness that the client is experiencing in this scenario is Stage 4. Stage 4 of illness is known as the advanced stage, where the patient requires surgical intervention for their condition. In this case, the client needs bypass surgery for their blocked artery, indicating that their illness has progressed to a severe stage.