I am not an immigrant myself, but I worked with many in the mid 2000s. My experience was that direct hire H1Bs did fine. The company is already shelling out lawyer fees for you, so presumably you're important enough for them to hang onto unless the situation is dire.
The company I worked for did also have H1B contractors whose contracts were terminated and some of those people left the country.
The company I worked for did also have H1B contractors whose contracts were terminated and some of those people left the country.