There wasn't anything that would guarantee survival, but there were things you could do to increase your chances. Even in the worst years, 1937-1939, the number of people who were "repressed" (contemporary term for those that were arrested and either deported, imprisoned, or executed) was between 1.5 and 2 million -- about 1% of the total population of the country. So your chances to survive we're pretty good -- unless you were one of the priesthood, or a relative of former czarist civil servants or officers, or rich, or Jewish, or a supporter of the wrong political movement du jour, or, funnily enough, being a communist party member -- in 1936-39 arrest rate among those was 50%!

Generally, not being one of the above, and not getting yourself noticed (e.g. making political statements in front of others, having a business or trading "under the table", being in someone's way (always a good chance of being denounced)), you would have very good chances to survive, above 99.9% I would say.

Sources: born there and know history; Conquest's "The Great Terror" (1990), Rogovin "The Party of the Executed" (in Russian).

If you were brave, in decent health, and had the resources, you could have done like the Lykov family and fled into the Siberian wilderness.

Of course, this was not easy, by the Lykov account, and most of the family did not survive to old age. On the other hand, they lasted altogether for several decades, which might have been more than if they stayed.

I hadn't intended to write so much on this so apologies if it comes across as somewhat disjointed. It started out as a reply to /u/Impstar2 but ended up rambling well beyond that.

Repression Deaths

Just a note on the figures. There's obviously been a huge amount of debate and controversy on these over the past few decades but the trend, as I can see it, has tended to favour lower numbers to those popularised by Conquest.

This debate became particularly acute when Getty et al published, in English, the official NKVD archival figures of 682,000 executions for 1937-38. Now, nobody accepts these numbers literally but they serve as a lower boundary to the estimates and are more useful than the previous estimates and guesswork that had informed Conquest's work.

With this in mind, today's estimates for 1937-38 (in English language literature) typically tend to range from 1-1.2m deaths. But, as I say, this is still a pretty contented area. Going beyond deaths and into the broader category of 'victims of repression' is even more difficult.

The important point is that while these numbers are high, and are higher when you add in Gulag figures, they do not represent a cull of the Soviet population in general. Soviet citizens would know about the purges but there was little to fear unless they were in one of the below victim groups.

Victims

/u/Impstar2 is right to point out the degree to which the elites suffered. The ranks of Communist functionaries was particularly gutted. There is a great story of two young graduates and junior party members (Ponomarenko and Chuyanov) being called up to party offices in Moscow only to be immediately packed off to the regions as the new heads of the Communist Party in Belarus and Stalingrad, respectively. In many ways this was a clean sweep of the pre-Purge party leadership.

But the Purges weren't an entirely elite affair, as was once thought. The majority of deaths were products of the 'mass operations', Order 00447 being justly infamous. In addition to those with suspect class backgrounds, at high-risk were those labelled 'socially harmful elements' (eg homeless, beggars, prostitutes, 'hooligans'), the intelligentsia and petty criminals. In addition, the 'national operations' targeted a range of suspect national minorities.

And, of course, there was pure bad luck. Getty provides the example of Turkmenistan in 1938 where "a fire at a factory became an occasion to meet 'quotas' for sabotage by arresting everybody who happened to be there and forcing them to name 'accomplices' (whose number soon exceeded one hundred persons)". He also notes that "it was always possible to round up people having the bad luck to be at the marketplace, where a beard made one suspect of the 'crime' of being a mullah."

But, while there is still debate on how far down the terror reached into society, for most people who never appeared on the state's radar there was, other than bad luck, little to fear. Workers in high-priority industries or with in-demand skills were relatively unscathed by the repression. (The draconian labour laws to tighten labour discipline didn't begin to appear until late 1938.) Workers were also protected to a degree by their enterprises, who were loath to lose skilled labour.

Even those that were at risk could sometimes survive by moving (so called self-dekulakisation) and getting work elsewhere. (Occasionally the neighbouring village was far enough, the Soviet state apparatus being uncoordinated enough that this sometimes sufficed.) This was after all a society continually in flux.

Sources

Michael Ellman's Soviet Repression Statistics is a nice summary of the 1990s literature on the topic, particularly the repression deaths.

The key post-Soviet paper on repression is Getty et al Victims of the Soviet Penal System in the Pre-War Years, which gave rise to a range of related polemics and articles. That also serves as the reference for 'bad luck'.

The story on rapid promotion during the purges came from Shelia Fitzpatrick's Education and Social Mobility in the USSR.

For general discussion around the purges and the nature of its victims, see Paul Hagenloh's Stalin's Police and Gerland and Werth's chapter on mass violence in Beyond Totalitarianism.

The note on 'self-dekulakisation' came from Mark Edele's Stalinist Society. Also useful, in understanding the reactions of ordinary people, is Sarah Davies' Popular Opinion in Stalin's Russia.