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.
In my case here is the solution.
I recorded motion capture using IPI soft, and the armature position was different in edit mode and pose mode.
Here is how I fixed it.
Find the bone which moves the whole armature. In my case or normally it's Hip bone that moves the whole armature.
Select the armature in object mode and go to pose mode, after this, select this Hip bone/Main bone, which moves the whole armature.
Open the Dope Sheet and select Action Editor, and below you will see all Locations keyframes. Example,
X Location (Hip) = keyframes
Y Location (Hip) = keyframes (In my case removing the Y location keyframes worked, because it's was the only keyframe, that was changing my armature location)
Z Location (Hip) = keyframes
After removing the Location keyframes, now select the whole armature and in pose > Clear Transform > All.
Go to object mode and play animation :)
"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.
I was facing the same problem. I tried something. first, go to edit mode, and remove the parent from the armature, then start posing the bone to relate to the mesh in edit mode, when done, start parenting every object to the armature in object mode. my armature was moving its location from object mode to editing mode, and that was annoying. I removed it, parent, in object mode and I noticed that the mesh is taking the location, scale, rotation of the armature whenever parenting it. so when we make its location etc. matches the location etc of the mesh. Both mesh and armature location must not change in both modes (object and editing mode). so that's what I came up with to solve my problem. hope that helps.