With the folded buttstock, you get the extended and folded buttstock options. The extended buttstock is described in the game as:

Extended for stability during aiming, but gives less mobility.

The folded buttstock is described as:

Folded for mobility, but gives less stability while aiming.

You can find this at the western edge of Koani province, near a Medication Raid side mission where you steal a plane. It’s in the middle of nowhere and I did a couple of runs by this location in my vehicle to run over some outlying cartel. There are a handful of sicarios guarding the plane which are easy to kill. The accessory case is inside a tent near the plane.

This buttstock fits some but not all sniper rifles, for improved handling at the cost of accuracy. Personally though, I favour accuracy over handling for a sniper rifle, so I don’t use this accessory.