"Quietly returned to their former lives" is probably hard to ascertain. That's because there were also substantial anti-Soviet partisan movements after the Germans were expelled. Even more numerous were people (not only Nazi collaborators) who just took the the woods for a while. What is certain is that the Soviets (and their client governments) offered numerous amnesties in order to reduce these anti-Soviet partisans and those who were just hiding. So, it's probable that the new Soviet-installed authorities didn't press too hard against former Nazi collaborators of low level. The new authorities were apparently more interested in solidifying a Soviet society, so those who were targeted were so more because of their potential to oppose the new regime.
Satiev says this much later in his book (pp. 198-204)
The [Soviet-installed] authorities viewed amnesties as a major means to
return from the forests draft evaders and deserters from collaborator units.
Most of these folk were not ideological enemies and did not plan to fight
the Soviets but could join the guerrillas out of desperation. The governments
of the western republics attempted to prevent this development with periodical
amnesties. Ukrainian leaders declared the first amnesty on 12 February
1944, when the Red Army had reoccupied only a fraction of western Ukraine.
They acknowledged that many “honest people” had joined the nationalists
and promised “all members of the so-called ‘UPA’ and ‘UNRA’ [ Ukrains’ka
Narodna Revoliutsiina Armiia (Ukrainian People’s Revolutionary Army), or
Sich ] who defect to the Soviet authority and honestly and totally terminate all
contacts with the Hitlerist OUN … full pardon for their grave mistakes and
crimes committed against the Motherland.” On 27 November, the Ukrainian
government offered a second amnesty; a third was given on 19 May 1945,
and three more were given before 1948. Even the last one, declared on 30
December 1949, when the resistance was dying, caused 8,000 fugitives to surrender.
Between official amnesties, Ukrainian leaders issued many appeals to
guerrillas to surrender and receive pardon. The Latvian Communist administration
duly enlisted rank-and-file deserters of the SS divisions who reported
to mobilization into the Red Army, and it declared amnesties for guerrillas
in September 1945 and August 1946. The Estonian government offered five
amnesties between October 1944 and 1955, and Lithuania granted them in
February and June 1945, in February 1946, and in 1947; the last two came in
October 1955 and March 1959. [...]
The amnesties crippled the resistance in every borderland region. In western
Ukraine, 18,917 persons surrendered during the first three months of
1945, or 22.8 percent of all “liquidated” fugitives, even though they knew
they would be sent to the front. This proportion rose when the war ended
and military service was no longer risky. The Estonian police claimed that the
amnesty declared in June 1946 prompted the surrender of about 45 percent of
the registered fugitives. For the entire period of armed resistance in Estonia,
the Soviet regime amnestied more fugitives than it arrested: 5,880 versus 5,796. Police files show that most of those amnestied in 1944–1945 were not
guerrillas but draft evaders who otherwise might have joined the resistance or
peasants who had fled to the forests from fear. Soviets sought to detach them
from the hardcore guerrillas and bring them back. [...]
Of all Lithuanians pardoned by 1956, 21.5 percent were guerrillas, and 78.5 percent were other fugitives. The police, however, emphasized that these figures did not reflect reality. The surrendering insurgents were ordered to
provide weapons and information on the units where they had served and
civilian infrastructure of the resistance. The police arrested those refusing to
betray their comrades. In contrast, draft evaders were not expected to have
weapons or to know much about the guerrillas. Hence most guerrillas who
surrendered in 1944–1945 claimed to be draft evaders, which the police had
to accept unless it could implicate them. [...]
Did the Soviet government keep its word about the amnesty of guerrillas?
In most cases, the answer to this question is positive. [...] No generalizations can be made about Soviet perfidy because the government
treated each case individually. Its decisions depended on the fugitives’
social and economic background and their record before and after amnesty.
Most peasants who claimed to have been involuntarily drafted by the guerrillas
or to have fled conscription and who later fought in the Red Army, militia,
or commando units received full pardon. Some insurgents – notorious leaders
of the resistance, former guerrillas suspected of subversion after their surrender,
those refusing to cooperate with the police, or belonging to wealthy families
or those whom the police simply picked to fill deportation quotas – were
If we infer a total from this statement of Satiev (2nd para quoted above):
18,917 persons surrendered during the first three months of 1945, or 22.8 percent percent of all “liquidated” fugitives
That puts the total number of "liquidated" (meaning surrendered/aministied/arrested or even killed) fugitives to some 82,969 in Ukraine alone. Which isn't "most" of the 300,000 members that the Schutzmannschaft supposedly had, but it's not a negligible fraction. If we're willing to infer that those who were not in this group just "quietly returned to their former lives", the claim could be considered true, but I haven't found a source to state it that way.