To fall on your sword is to kill yourself rather than live with dishonour. Or, in these modern times, to take responsibility publicly for something even if it will lead to loss of office or loss of reputation.
In an honest culture, the XXXX would stand up and take the blame. They would admit that this whole debacle was their idea, and that they were being deceptive when they sold it to the XXXX people. They would offer sincere apologies and then fall on their swords as a way of making amends to their fellow countrymen.
Yes, it does. In Roman times, you fell on your sword so that your family would be spared any harm from your disgrace-- it was thought unseemly for the Emperor to confiscate wealth from a dead man, let alone his widow and children.
So "falling on your sword" was a generous and honorable act made necessary by adverse circumstances-- which weren't often fair. Nowadays the beneficiary of such an act is usually a higher-up, and the generous blame-taker is something of a dupe or scapegoat. The baby thrown off the back of the sleigh, to appease the pursuing wolfpack.
1 Samuel 31:4-5
Saul said to his armor-bearer, "Draw your sword and run me through, or these uncircumcised fellows will come and run me through and abuse me." But his armor-bearer was terrified and would not do it; so Saul took his own sword and fell on it. When the armor-bearer saw that Saul was dead, he too fell on his sword and died with him....