If the US immigration system were working properly, we would not have residents who do not have a solid legal basis for residence in the US.   In many cases that would also mean that they would not, in fact, reside in the US.   But I do not think that is what  Sen. Kaiser means by "protecting those who have been failed by a broken immigration system".   I think she actually means something like, "being kind to those who have come to the US without complying with the immigration system", which is a perfectly fine sentiment but which is seldom spoken of in an honest and straightforward manner.   If we can't have straight talk, we are unlikely to fix the "broken" system.