关于and，but前有逗号到底要不要补充主语？纠结纠结~~请教请教~~~

prep223
After several years of rapid growth, the health care company became one of the largest health care providers in the metropolitan area, while it then proved unable to handle the increase in business, falling months behind in its payment to doctors and hospitals.
A. while it then proved unable to handle the increase in business, falling months behind in its payment to
B. while it then proved unable to handle the increase in business and fell months behind in its payment to
C. but then it proved unable to handle the increase in business, falling months behind in its paying
D. but then proving unable to handle the increase in business, falling months behind in paying
E. but then proved unable to handle the increase in business, falling months behind in paying
答案选E，不是不理解。
我的问题是，不是有条定律是两个句子并列，but或and前若有逗号隔开，第二句的并列或者转折要加上自己的主语，即便是和第一句重复的主语，做到好几道都是这样的情况。
但有时又碰到不要加主语的，比如上面这道，那到底什么时候要补充主语什么时候不要呢？？？
我混乱了。请NN帮忙解答。

不胜感激，撒花撒花~~~~~~