I wish to die while still at work, knowing that others will carry on what I can no longer do, and content in the thought that what was possible has been done.

1. 划线部分是 wish to die... 的原因状语。因为后面的原因，才希望怎样。

2. that what was possible has been done 是 the thought 的同位语从句。

3. what was possible （主语）has been done （谓语） （过去可能的事情我已经做到了）

现在分词 knowing 作“原因状语”，是最常见的用法。又如：

Parents often feel helpless, knowing that all the cuddles in the world won't stop the tears 

父母经常感到无能为力，因为他们知道无论多少次拥抱也无法止住眼泪。

《柯林斯高阶英汉双解学习词典》

He took his time answering, knowing that he must select his words with great care. 

他意识到自己必须言辞谨慎，于是不慌不忙地回答着问题。

《柯林斯高阶英汉双解学习词典》