What is your definition of a "big film"? Virtually all of the movies he has starred in the past 20 years have been money makers........
Actors sometimes get to play in big budget films which are star vehicles just for them. They’re offered these roles when they are household names because their very presence sells tickets (and viewers will instantly identify with their character, making the script more effective.)
When their drawing power ebbs a bit, they’re offered secondary roles in big budget films.
When their drawing power dwindles, they’re offered roles in indie films.
When they wish to boost their drawing power, they often pull publicity stunts to get back in the public eye.
I don’t follow celebrities so I couldn’t tell you where Neeson is on his career path.