Here's a photo showing a very simple and inexpensive way to keep hangers from jumping off the closet rods when traveling.
These are the same little rubber gizmos I use on the "S" hooks on the safety chains to keep them from jumping off the receiver.
I paid 99-cents for the pair at a local boat shop.
Online at Amazon they are ridiculously priced. Some places want $7 for the pair and $7 to ship them. Others places will ship them for "free" but want $14. What a racket!
Hangers designed to stay on the rod cost $9 for a half dozen plus shipping.
Truth be told you can make them yourself for pennies with an old inner tube and an x-acto knife.