The word "involved" here is an adjective; it modifies "people" by indicting which people are being discussed.
Both "involved people" and "people involved" might be said by fluent or native speakers, and in this case the meaning is much the same. However "the people involved" seems more natural to me, and i think it is the more frequently used.
In some cases of {adjective}+{noun} one order has become a set phrase with a specific meaning, that the opposite order does not share.
For example:
I think the working people are content.
refers to a broad socioeconomic category. On the other hand, the seemingly similar:
I think the people working are content.
refers to specific people doing specific work.
Other examples:
- The fast ships are tied. (There is a race and no one is winning.)
- The ships are tied fast. (The ships are strongly attached, provably to a dock or mooring point.)
- Green beets are tasty. (the speaker likes unripe beets.)
- Beet greens are tasty. (The speaker likes the leaves)
- faded jeans (refers to the pants after they have lost their color)
- jeans faded (refers to the process by which the color is lost.)