He went to work sick, ... (Para. 3)
Meaning: He went to work even when he was ill.
Here the adjective "sick" should be understood in the context as "when he was sick".
Look at the use of the adjective "hungry" in the following example:
He went to bed hungry last night. 他昨夜饿着肚子上床睡觉。
More examples of this kind:
The tomatoes should be picked green. 这些西红柿应该青的时候摘。
I can't drink it hot. 它太烫, 我没法喝。