In N. America, the Americans, the most generous conquering force in all of history, did not exterminate the tribes. Yes, they conquered and sent them to Oklahoma and other desolate places, but they still received some land. A great deal compared to what happened to their brethren of Incas, Aztecs, Mayans etc. . .

One often overlooked factor that people don’t like mentioned, is that it was the tribes that sided with the French in the 7 Years War against the colonies, were punished much harsher than the tribes that were allied with the colonists.

So while much is made about the Trail of Tears, little is discussed as to why some tribes were treated better than others, and the answer is because some tribes allied with our enemies, some tribes allied with the colonists, and that decision determined much of their fate.

But to directly answer your question, they gave up their land instead of their life.

They never “gave up” any land. They either traded something for it which usually ended up being a pretty lopsided trade or they were forced off of it.