Comma between subject and verb

Never place a single comma between the subject and the verb. If you use apposition, then you may place two commas between the subject and verb, as in: "Janet, a student at the university, said she had the time of her life", in which the subject "Janet" is separated by two commas from "said."

In this case, however:

The first sign that democracy is dying, is that corruption is rising.

the author has mistakenly placed a single comma between the subject, probably because she felt the subject was rather too long (in fact, it is long, and it even contains its own verb, which confuses things):   The first sign that democracy is dying.

The sentence should therefore contain no commas at all:

The first sign that democracy is dying is that corruption is rising.

Therefore (first version wrong, second right)

The fact that we are all connected through technology, is a double-edged sword.

--> The fact that we are all connected through technology is a double-edged sword.

The idea that everyone should have equal opportunities, is a cornerstone of modern society.

--> The idea that everyone should have equal opportunities is a cornerstone of modern society.

The belief that hard work eventually pays off,  is a common misconception.

--> The belief that hard work eventually pays off  is a common misconception.

If you think that  it's a bad rule, join the Old Fogies' club.   It used to be different. English once used far more commas  than now.