Most high-risk immigrants today (illegal immigrants from Mexico, boat people from various countries) are escaping places where they suffer political oppression, horrific living standards, or extremely poor economic opportunity. But as far as I can tell, the English-speaking whites of the United States who migrated over the Appalachian Mountains and into the West were taking great risks despite coming from relatively prosperous locations on the Eastern portion of the continent.
For instance, I was looking at the history of the "Chickamauga Wars" http://en.wikipedia.org/wiki/Chickamauga_Wars_(1776–94) which were fought over Cherokee resistance to white people migrating from North Carolina and Virginia. Repeatedly, parties of settlers would travel on flatboats down the Tennessee River knowing there was a major chance that they would be attacked and possibly overwhelmed by the Chickamauga Indians near where Chattanooga is today. With the violence lasting almost two decades, the settlers must have been quite conscious of the extreme risks involved in trying to reach the fertile lands west of the Cumberland Plateau. But the areas they were travelling from, such as the Shenandoah Valley and the North Carolina Piedmont, also provided good opportunity. So why would they take such risks which, by modern standards, would seem quite insane.
Immigration, whether it was transatlantic, transpacific, or trans Appalachian, was always the result of a complex "push-pull" equation. And there was always great risk. Circumstance at home needed to be bad enough and the lure of opportunity (which in the great periods of immigration generally meant free or cheap land) had to be great enough to inspire the trek. The American West simply looked too good for many to pass up. At the same time, many did not risk it. Some who went died or failed. But some who didn't risk it died or failed.
Most people that moved west were first generation immigrants and in many cases 'fresh off the boat.'
At the time of westward expansion, land ownership was out of the reach of most immigrants had they stayed in Europe. A lot of these immigrants moved to America and then moved west to make use of the Homestead act and finally become landowners - something that would have been out of their reach in Europe.
Moving to the frontier provided a way to build wealth that they never would have had in Europe or in in the huge east coast cities.
The frontier also provided a lot more individual freedom and acted as a 'release valve' for people who didn't want to be under the government's thumb or fit into typical society - the biggest example of this is the mormons, but another very common group of people that moved westward to get out of typical society was inter-racial couples. Interracial marriages were more common in the midwest because of this.
*side note: most people who tried to homestead failed because they weren't prepared (skill-wise) to actually farm.
I would point out that the Mormons suffered harassment and persecution at settlements they had established in the East (New York, Ohio, Missouri, Illinois). They fit very well your current profile of a high-risk immigrant.