Russian (total) enserfment is a fairly late* phenomena for a few reasons and is actually a bit ironic. I will explain irony in a bit but first it's important to understand what was going on with Muscovy state. Muscovy (Kievan Rus then) became Christian nation in the 10th century but it chose Orthodoxy. This will play an important role later on during the Reformation because there was no such thing per se in Russia, there was a schism (raskol) within the Russian Orthodoxy but it would not mirror the Western Reformation.
Reformation in Western Europe was not only religious, it was also political and Protestants tended to be of a middle upper class. Because of this some scholars argue that post-Reformation influenced the beginning of modern capitalism (Max Weber, "The Protestant Ethic and the Spirit of Capitalism.") There is much to be said about capitalism, Reformation and all the intricate details about it but it's beyond the scope of this post.
The key points are that Western development was different, there was religious revolution, and economic shifts. Take the Dutch for example, after the independence they focused on commerce and other nations later on took the lead by investing and getting revenue from international maritime trade, England, France, Spain.
When you look at Muscovy, there is a different evolution. Kievan Rus was actually and arguably more developed that the Western counterparts at the time. Kievan princes married off their daughters to Western kings, Kiev was a big cosmopolitan city, and Rus relied on trade a lot and supplemented with agriculture only when needed. Peasants were not enserfed and locked in to one place at this point, they could leave and move to work any land they wanted.
So what happened? The Mongols... Rus' got cut off from the Black Sea and key trading posts, cities burned down, parts of Rus became controlled by the Mongols and the far Western ones were under Poland (Polish-Lithuanian Commonwealth) eventually later on. Under the Mongol rule Russia suffered greatly and missed out on general European development. There was a certain intellectual black out and stagnation.
Few hundred years later, as mentioned previously, Western Europe is going through political changes. Russia (Muscovy) managed to survive the Horde and started to expand it's territory. Ivan the Terrible becomes the absolute monarch in Russia and quite a few reforms are being implemented. And here is where it gets interesting. For one, as Russia is expanding the need to protect the borders becomes higher, so some incentives are being placed in order to retain more people on the border. Peasants got out a few things out of relocating to the borders (Belgorod Line for example). There were no landlords to worry about or pay rent to. Fugitive peasants were rarely returned to their old place by the government officials. Peasants could significantly to raise their income by cultivating a very rich soil (chernozem) at the southern borders. In return they could be recruited for military service.
I've mentioned a fugitive peasants and that they were rarely returned to their old landlord. At this point the enserfment was not total. They could still move and here is how Brian Davis puts it:
the peasants were bound to the land with the repeal of the right to move on St George’s Day until further notice and the five-year statute of limitations on the filing of suits for the recovery of fugitive serfs. What may be called ‘the Soviet’ explanation for this was that the government was so terrified by first the Khlopko uprising (1601–3) and then the Bolotnikov uprising (1606–7) that it lacked the spirit to repress the peasants any further.
And there was another reason why a landlord would want to recover his fugitive peasant. It was because of poor paperwork... Here is an example: let's say you have 1000 peasants working, 50 ran away. Some government official comes up to you and asks you to pay the appropriate fees and tells you that you have 1000 peasants so you owe such and such amount of money. You say that the paper work is wrong, you have only 950. Tough luck, outdated or not outdated paperwork, you pay. In short, what I am getting at is corruption and inefficiencies in the system.
Here is a bit of an irony. Towns people were the free folk, working class, not necessarily peasants. They had to pick up the slack for any bureaucratic errors in the records. So in 1637 the middle class as we would call them, started a petition for enserfment of peasantry. At first the was another solution, extend the limit time to recover the fugitive peasant. Because of corruption it wasn't enough, as mentioned before, fugitive slaves were needed to work land on the borderlands so officials would just ignore these requests. Other landlords would simply hide their peasants and not report them. So there goes another petition, and another, and eventually the Russian state decided to just bound the peasants to the land... and the towns folk... the very people who petitioned for enserfment of peasants but they got the blowback too.
And this is how we got Russian enserfment in the ~17th century when the Western Europe was done with theirs.
*Just to point out, I am referring here to the 'second enserfement' in Russia that didn't end until Alexander II's reign. I don't want to give an impression that Russian enserfment only started in the 17th century.
Sources: "The Age of Religious Wars" by Richard S. Dunn, and "Ivan the Terrible" by Maureen Perrie, plus a quote from Brian Davis.
I though PLC was not yet formed when Mongols invaded?