[6] In 1923 he was arrested for "illegally crossing borders", a label which covered smuggling or for being a merchant who was too successful for the Soviet Union to tolerate.

[15] His reputation is, however, controversial: Aleksandr Solzhenitsyn claims that Frenkel personally invented the notorious you-eat-as-you-work system, also known as the nourishment scale, which destroyed weaker prisoners in weeks and would later cause uncounted casualties; on the other hand, a wide range of Russian and Western historians dismiss the many stories of Frenkel's omnipotence as legend.

[15][16]: 121  Journalist Anne Applebaum states, "Even if Frenkel did not invent every aspect of the system, he did find a way to turn a prison camp into an apparently profitable economic institution, and he did so at a time, in a place, and in a manner which may well have brought that idea to the attention of Stalin.

[21] At the same time random cruelty inflicted by the captors on the captives decreased: such behaviour was now considered inappropriate in an institution which valued trudosposobnost - 'the capacity to work' - above all.

[21] Some remembered him as a dandy who had a good head for figures and, according to Maxim Gorky (who visited and approved Solovetsky Islands in June 1929) and others, a perfect memory.

Others hated and feared him: in 1927 the year of his early release, in one of the first foreign publications about the Solovetsky Islands, it was written by the French anti-communist Raymond Duguet that, "thanks to his horribly insensitive initiatives, millions of unhappy people are overwhelmed by terrible labour, by atrocious suffering.

"[25] He was accused in 1928 by his comrades in the Solovetsky Islands Communist Party cell of organising a personal network of spies "so he knows everything about everybody earlier than everyone else.

"[26] Before his early release was granted, Frenkel had organised and then managed the Ekonomicheskaya kommercheskaya chast, the Economic-Commercial Department of SLON, through which he tried to make the Solovetsky camps not merely self-supporting in accordance with the concentration camp decrees but profitable with the result that they began to take work away from other state undertakings: an element of competition remained in the Soviet Union in the 1920s and Frenkel took advantage of this.

[13] With Frenkel running its Economic-Commercial Department, SLON had already outbid a civilian forestry undertaking and had won the right to fell 130,000 cubic metres (4,600,000 cu ft) of wood in Karelia.

[13] SLON had also become a shareholder in the Karelian Communal Bank, and was tendering for the construction of a road from Kem to the far northern city of Ukhta.

[20] From the outset the Karelian local authorities had been unnerved by all of this activity, not least as they had initially opposed the creation of the camp altogether.

[31] Anne Applebaum wrote:"The argument over the profitability, efficiency and fairness of prison labour was to continue for the next quarter-century [...] in the mid 1920s the Karelian local authorities were not winning [the argument] [... and] although as late as 1929, the camp was in fact running a deficit of 1.6 million roubles - quite possibly because OGPU stole from the till - Solovetsky's supposed economic success was still trumpeted far and wide.

[citation needed] On April 28, 1947, Frenkel was discharged from his duties for reasons of health, and was awarded a service pension.