the punishment of theft

What about the prescribed punishments in the law of Islam, for example the punishment of theft?

The issue is not just theft, but rather what is associated with it.

In the saheeh hadeeth, the Messenger of Allah (may the peace and blessings of Allah be upon him) said: "The hand of the one who betrays a trust, the robber and the pilferer is not to be cut off".
Applying the precribed punishment of theft is not just for taking money, but because of the crimes associated with the theft that may reach the extent of murder.

If a man takes a thing under his charge, like the case of a guard and a storekeeper, then his hand is not to be cut off
If a person stole a fruit from a tree, his hand is not to be cut off.  The Messenger of Allah, may Allah bless him and grant him peace, said: "The hand is not cut off for fruit hanging on the tree and for sheep kept in the mountains. (Muwatta Malik) 

In his book Al- Sunan Al-Kubra, imam al-Bayhaqi narrated that Ali ibn Abi Talib (may Allah be pleased with him) said: "the one who stole money from the public treaury may not be cut off."

It is not just the case of robbery, otherwise the hands of the previous categories would have been cut off.

However, since these three men were most likely to carry out their crime without endangering the lives of the safe people, this prescribed punishment was not applied on them. 

 Stealing the fruit and the sheeps in the mountain is far from exposing the safe people to danger. Therefore,  prescribed punishment was not applied on them.

Question: If a person is robbed and confessed his crime to the Judge, will his hand be cut off?
Answer: The judge will expel him.

 
Abu Umaiyah al-Makhzumi (may Allah be pleased with him) narrated: A thief who has made a confession was brought to the Messenger of Allah (may the peace and blessings of Allah be upon him) but no goods were found with him. Allah's Messenger (may the peace and blessings of Allah be upon him) said to him, "I do not think you have stolen!" The man replied, 'Yes I have.' The Prophet (may the peace and blessings of Allah be upon him) repeated it to him twice or thrice, so he gave his commands concerning him, and his hand was cut off. He was then brought to the Messenger of Allah (may the peace and blessings of Allah be upon him) who said to him, "Ask forgiveness of Allah and turn to Him in repentance." The man said, 'I ask Allah's forgiveness and turn to Him in repentance.' The Messenger of Allah (may the peace and blessings of Allah be upon him) then said three times, "O Allah! forgive him." compiled by Abu Dawud, Ahmad and An-Nasa'i with a trustworthy chain or narrators, and it is Abu Dawud's version.

Al-Bayhaqi narrated with a good chain of narrators that: "A man came to 'Ali, may Allah be pleased with him, and said to him, I stole, so Ali expelled him".

Abu al-Darda said to a woman who stole: " O Salama did you steal? Please reply in the negative.

On the authority of 'Ataa, he said: "During the time of the righteous predecessors when they cought a thief, they used to say: ' did you steal? Please reply in the negative or say I do not know.

Ibn Abi Shaybah composed a chapter in his book Al-Musanaf under the title: when they cought a man, they used to say: ' did you steal? Please reply in the negative.
It was narrated that Abu Mas'ood said: they caught a man who stole something. He asked him: did you steal it? Say, I found it, he said: I found it. Therefore he was released. 

It was narrated that Abu Mutawakil said that when Abu Hurayrah was the leader of the believers, they caught a thief. He asked him: did you steal? Did you steal? Please say no. he repeated it two or three times.

On the authority of 'ikrimah ibn Khalid, he said: they brought a thief who confessed to 'Umar. 

Yet 'Umar said:' I do not think that this hand belong to a theif, It is not a hand of a thief. The man said, "By Allah I am not a thief." 'Umar released him and did not cut off his hand