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Guilt? maybe in his own mind. After his death in 1953 it was discovered that he had kept a 1938 note in his desk from Nikolai Bukharin, who was a former ally and one of the chief target of the Moscow show trials, pleading for clemency before his execution. However he did not express guilt in the company of other people with regards to political murders (though some of the people around him did observe that he was guilty over his wife Nadya's suicide).
Sadness? Of a sort.
Stalin in his old age was lonely, mainly because his old, pre-war social circle composed of his in-laws had being decimated by the purges. His daughter had became increasingly estranged from him, largely due to the poisoned social atmosphere of the Kremlin. He was desperately seeking friends and companionship. A difficult task, as almost everybody in the Soviet Union was terrified of him. Khrushchev described dealing Stalin in his later years as like dealing with a lonely elderly relative whom he cannot offend and was constantly seeking company. He said that Stalin would call him or other members of his inner circle for a something that would require two minutes to explain, but then stay on the phone for another hour.
He would also "invite" his inner circle to all-night dinner, drinking and movie-watching parties, which was taxing on his comrades who were forced to run the Soviet government during the day and then spend all night not getting sleep to keep Stalin company. Not to attend would, of course, be unhealthy for one's political career to say at least. Stalin also missed the days of his youth and at one point suddenly decided to invite some of his friends from his Seminary school days to the Kremlin. They stayed with him for a week (terrified the whole time) and joined Stalin in singing loud drinking songs at his nocturnal dinner parties.
However, it is doubtful that Stalin ever truly appreciated how political murders had poisoned his personal life and relationships. Nor did he ever stop his paranoid behavior and continued to carry out purges of the Communist party and people around him until he died.
Source: Court of the Red Tsar by Simon Montefiore
On Stalin's team, years of living dangerously by SHEILA FITZPATRICK
Dmitri Volkogonov was a Soviet General who had access to many of the secret archives. After the Fall of the SU he was a liberal supporter of the new regime. He wrote some great biographies of the Soviet Leaders. In his Stalin tome he describes the thousands of appeals that Stalin received from people sentenced to death or the Gulag.
He notes that Stalin via his famous blue pencil rarely showed any mercy or ever commuted a sentence. Nothing personal moved him. In fact he seemed to delight in tricking leading high ranking prisoners to think that if they confessed he would show mercy -- but then, of course, he did not.
Once in a while he would commute a sentence but only when the appealer made some sort of practical argument. To take one example, a factory manager was arrested but then wrote a letter to Stalin claiming that the other people in the factory who were running it now were idiots and he needed to return so it could be run efficiently. Stalin commuted his sentence and sent him back to run the factory.
https://www.amazon.com/Stalin-Triumph-Volkogonov-published-Hardcover/dp/B008TA1NYK