The Chinese made several military incursions into Xiongnu territory, and over the course of centuries the people split into several groups. One group, the Western Xiongnu fled west into what is now accepted as Central Asia in roughly....100 bce, and not long after that we lose track of them. When people speak of a connection that is the group "that became the Huns". This was at one time highly speculated, and while fun to discuss now, it isn't taken as seriously due to the serious lack of evidence. I cannot give you much more info because I've only been seriously researching this for the past month or so, but I will give you my source: The Empire of the Steppes. It's old in terms of historiography, from the 1930s or so, but is still considered a standard reference.