Before that, you technically had to leave the country the day you were laid off. Never mind that you might have a house a family and might have been living here for more than a decade. You would officially be staying illegally if you didn't leave right away and it would jeopardize your chances of getting a visa in the future.
It's only through an historic odd mix of good pay and relatively laxer immigration rules that the US managed to attract a large pool of talent in the 80s, 90s and 00s. Students from my college who are about 5-10 years junior to me no longer consider it a viable place to plan a long-term career in due to the extreme precariousness of visa holders' life situations in the US.
Politically speaking we have little to no power in numbers so neither politically party really cares. Typically it's the Democrats who are pro-immigration, but in reality they don't care much about H1B style immigration and are in fact likely against it due to American tech unions hating H1Bs, while we have unlikely allies in some Republicans because our presence benefits big companies. Common sense solutions standard across the world (such as skill-based / point-based systems) are looked down upon, while we keep getting kicked around on the political playground.