Many RVs use some form of locking latch or glide track to prevent that. The rest have a manual lock bolt of some kind installed. Child safety locks are one common aftermarket solution, but your HR almost surely has some sort of latch built in.
A typical drawer latch is a friction device that can be opened simply by pulling extra hard. Here are a couple examples:
https://www.amazon.com/dp/B014HXSS1I/
Satin Nickel Plated Brass Bead RV Catches
Some others have an indentation in the drawer slide that the glide wheels settle into and a lift & pull motion is used to overcome the latch.
Perhaps another HR Vacationer owner can tell you what type of latch it has, but it appears yours are not working properly. They can be repaired, of an alternate & improved method installed.