After clearly stating that as president he had no power to change immigration law, then-president Obama went ahead in 2012 with
Deferred Action for Childhood Arrivals (DACA). Obama himself referred to DACA as his "
action to change the law," a power vested in the legislature, not the executive.
In 2010,
Obama told an audience of amnesty proponents that he's "not king" and "can't do these things just by myself." In 2011, he explained further, "that he couldn't "just bypass Congress and change the (immigration) law myself. ... That's not how a democracy works." And in 2012, he did it anyway.
Then-presidential candidate Trump campaigned on ending DACA, and in September, he announced
his decision to end DACA after giving Congress six months to pass it into law. Passing DACA or some equivalent into law is perfectly within the purview of Congress.