Is there anything that doesn't allow the people of DPRK to cross the North Korea-Russian border?
The border line between Russia and DPRK is very short and goes by the fairway of river Tumannaya (Tumangan). There's only one bridge with a railroad. No passengers, only goods trains.
On the Russian side there are a lake, a village and a border post named Khasan. By the way, in 1938 that place was an area of conflict between the Soviet Union and Japan, see Battle of Lake Khasan.
This is a short Russian TV material about Khasan border post. The soldiers say that the Koreans trespass the border quite often, because they practice illegal fishing and such. But they see it rather like a routine work.
UPD. As @gerrit noted, in the last couple of years the situation with passenger trains was changed. So now we have a passenger train Moscow-Pyongyang.
They can cross the border but why? Russia does not accept illegal immigrants, and it is usual practice in the world, the only exceptions in the world where immigrants were welcome are possibly East-West Germany border and South-North Korea border.
Besides, why even they would want to make it to Russia? The Russian areas in the Far East are underdeveloped, and have poor infrastructure, they would not find good job etc. There is no reason to move to Russia.