I have a rig, and when I select the Armature or the Model, and go to edit mode, they move position. They just go to the left, and they come back in object mode.
In Pose mode make sure you are in "Pose position" .
In rest position it will go to the objects original position and origin point
Also , Edit mode doesn't effect the animation / Pose , so when you go into edit mode , the armature will also go to the objects original position and origin point . Edit mode is only for moving vertices/faces/edges and bone origin placement
I had this same problem too! I tried all of these answers but none helped, I finally figured it out. All you have to do is go into pose mode and select each bone individually(you might be able to select all but I didn't try) and press "Ctrl+A" and apply location, rotation, and scale. If this doesn't help for you I am very sorry. It worked for me.
"Clear Transform" in Pose Mode helps to reset the bones transforms to the "Pose Position" in Edit Mode.
It clears any Pose Mode transforms and resets the armature to the Pose Position.
1 Edit Mode -> .Select entire armature (works even by selecting only the transformed bones)
2 Pose Mode goto -> Pose ->Clear Transform -> All
You may loose all animation and have trouble reapplying actions (newly applied actions will be relative to the OLD rest position), but if your Pose Mode is a T-Pose, Select->All in Pose Mode and go to Pose -> Apply -> "Apply Pose as Rest Pose". Then both your Rest Position and pose in Edit Mode should that be exactly the same as your T-Pose.
I believe this gives you the ability (or forces you) to redo your animations with a rig whose Rest and edit mode matches the T-Pose.