Why isn't there a verb before
The insurer has the right to the advantage of every right of the assured which will diminish the loss he has been forced to bear.

What's meant by"has the right to the advantage"? To use the advantage or what?What does he refer to? insurer or assured?

Question

Why isn't there a verb before
The insurer has the right to the advantage of every right of the assured which will diminish the loss he has been forced to bear.

What's meant by"has the right to the advantage"? To use the advantage or what?What does he refer to? insurer or assured?

Answer

It's a poor rewrite. You would do much better by using native English websites instead of Chinese websites (yes, I've found the source for your quotation).

Replace "has the right to" with "is entitled to". The sentence you have has been simplified a little, and it's made the sentence even more confusing.

As for which person "he" is... as I said, it's poorly written. We can't know.