Escapes happened; its only natural for people to want to escape imprisonment, and no system is every totally secure. However consider the following:

• Most camps were remote, as in they had no access to things like roads. The only way in to many was rail or plane, which were controlled by the government;

• Even so, they were often concentrated in a region, so the immediate area (relative term) would be full of guards, military, police, or other government forces;

• For those not associated with the government, there were large financial incentives to report escapees; failure to do so could mean imprisonment for the villagers themselves;

• Finally, the geography. Siberia, and the other major regions of the gulag (Arctic and Kazakhstan) are awful to try and traverse; in the summer its impassable marshland, while the winter is freezing temperatures. There is also a lack of freshwater, and lack of adequate shelter to shield one from the extremes of weather.

That said, yes prisoners escaped. Anne Applebaum's Gulag: A History has an entire chapter titled Rebellion and Escape, which is the primary source I'm using here. She notes that the early years of the camp system was the best time for escapes: in 1930, for example, she writes that 1174 prisoners were captured trying to cross the Finnish border (there was a large concentration of camps near there at the time). By 1932 that number was 7202. There is no number of successful escapes, and I will not speculate here, but you can draw your own conclusions on to the rate of captures to escapes. But to give you an idea, she writes that in 1933 the total number of escaped prisoners in all camps was reported by the administration as 45,755, with 28,370 captured (she also mentions that as this was a self-reported statistic, its possible its not accurate). This number did not decrease as the years went on, either; in 1947 10,440 tried to escape the camps, with only 2894 caught. The Long Walk, the book the film was based on, is also noted, but there are doubts about whether it is a true account or not.

So in short, yes prisoners escaped, though in the context of millions (at the peak of the Gulag), it was not a large number who did so. And unfortunately I don't have numbers for those exclusively based in Siberia, but would not really think it that different than the others; none of the camps were exactly in ideal locations for escape.