As a kid, I read the story about the thirty years war. In it, a man is sentenced to die by hanging for crimes upon the civil populace. However, the rope breaks and an old tradition of that the crime is considered forgiven and served if the rope or branch that the rope is hung upon breaks (or three times in a row drunken executioner).
I also recall a reference to that those who had stolen from the church was hung with a chain to avoid them getting a pardon that way.
Are there any truth to this tradition?
Could you specify which country this supposedly took place in?
I only know about English legal history, and I'm not familiar with a similar case. The closest I can think of is John Smith, who was hung in 1705 (about fifty years after the Thirty Years War). He survived being hung for 15 minutes, until the crowd took pity on him, and demanded he be spared. We know about the case because his story was printed, along with his account of what being hung felt like. Here is an online copy: http://www.exclassics.com/newgate/ng104.htm
There have also been cases of people who were hung reviving after they were supposedly executed. In some cases, these people could be given a reprieve, but they could also be hung again. Even if reprieved, they generally wouldn't be pardoned, but would be placed in prison or transported.
It is also worth noting that there would be no legal requirement to pardon someone whose rope broke. British law specified that a person would "suffer death by hanging" until the WWII era, when it was changed to "hung by the neck until dead." Both of those pretty clearly specify that the person had to be killed, rather than simply hung.
It's hard to prove a negative, so it's entirely possible there was a local custom to that effect somewhere, but it doesn't seem traditional to England as a whole. If there was a tradition, it had no legal basis.