Your question is incredibly misleading, at best.
No Democrat supports "free healthcare for illegals". That formulation sounds like they want to give a benefit exclusively to illegal aliens. No Democrat, anywhere, supports that. What Warren, and most of the other Democratic candidates, support is a public option for health care (for some of them, this wouldn't be an "option" but would effectively replace private insurance). In several of the case, not all IIRC, this program would extend to illegal aliens as well. This is not "free healthcare for illegals" but free healthcare for everyone.
Your formulation reminds me of the old joke on the Simpsons "Just miles from your home, hundreds of men are given weapons and trained to kill. The government calls it 'the Army' but a more alarmist name might be 'the kill bot factory'."