The idea of a society so strictly divided between the very rich and the very poor reminds me of Freejack, even if this concept is in the background, rather than the main theme.
The movie also features a lot of chases and action, but it is an early '90s movie, so maybe it is a bit too old to be the movie you're referring to.
In 2009, the super-wealthy achieve immortality by hiring "bonejackers", mercenaries equipped with time travel devices, to snatch people from the past, just prior to the moment of their deaths, for use as substitute bodies. Those who escape are known as "freejacks" and are considered less than human under the law. In this dystopian future, most people suffer from poor physical health as a result of rampant drug use and environmental pollution, making them unattractive as replacement bodies.
And about the chase part
Alex spends much time escaping the clutches of Victor, a ruthless pursuer who nevertheless lives by a code of honor,