"Decency" is a word which seems to have a fairly broad definition. It seems associated for the most part with propriety; conduct which conforms to what is considered proper, generally in a moral sense. Those without decency act in such a manner as to call into question their worth or quality as acceptable members of society. Someone with no sense of decency acts dishonorably, and fails to conform to standards people are expected to meet in their dealings with others.
A famous example of the use of the word is what took place in the course of hearings involving the infamous Senator McCarthy of Wisconsin, known as the Army-McCarthy hearings. These addressed McCarthy's claims that the army was filled with Communists.
Joseph Welch was the lawyer for the army. During one of the hearings McCarthy revealed that a young member of Welch's staff once signed a petition supportive of the Communist Party. There was apparently no claim he joined the party at any time, but McCarthy made the statement in an effort to assert that the staffer and others defending the army, including Welch himself, had Communist sympathies.
Being associated with the Communist Party in those times could ruin a career or even life. Welch famously chastised McCarthy in response, accusing him of character assassination of the staffer for no good reason and asking "Have you no sense of decency, sir, at long last?" It was a dramatic moment, and it's considered that this response triggered the decline in McCarthy's popularity and influence.
As a result of this moment, which was made during a televised hearing and was widely replayed, McCarthy was thought by many to have acted improperly, in a dishonorable manner; to have been unjust and cruel in an effort to score a trivial point. He acted indecently.
I'm uncertain whether something similar could take place now. Certainly if it did now all would know of it and would see it almost instantly, but I don't think it would have the same impact. That's because I feel many of us, and most and perhaps all of those who currently dominate and influence our plutocracy, have no sense of decency. As a consequence, they can't be shamed as others were in the past.
What we see enacted now is being done not merely without thought but as if considerations of justice and honesty are no longer of any importance. There are no standards which apply, or at least no standards which those in power believe people think should be met. Moral conduct, and in particular honorable conduct, is neither expected nor thought to be admirable in these sad times. It is only important that a policy or agenda is advanced, or what is desired is acquired, without incurring a loss.
We may have become an indecent society, or nation, or civilization.