What you are describing (dropped fetlocks) is usually due to degenerative suspensory ligaments (DSLD). Usual signs include hind limb lameness (both hinds), swelling over the suspensories, and thickening of the ankle. As the fetlocks begin to drop, the horse's conformation changes. The horse will become very straight in the hind end.
The farrier is the first person who noticed it on my old horse.
Remember it is also normal for the pasterns to drop as the horse moves (to absorb the impact). The difference is with DSLD, the ligaments weaken and no longer spring back. It's like a rubber band that gets over stretched.
It is most noticeable at the walk and standstill. Some horses can have it and still be sound, but it is a degenerative disease.
It is very common in older horses. Now that I know what it is I've seen at least 5-6 horses with it. It is can be a slow onset, or quick onset. My mare probably had it for years without anyone knowing. Everyone assumed she had hock issues.
If she did have it, I would keep working her lightly as long as she is sound and not having any major swelling. The muscles need to be strong to make up for the weak ligaments. Stall rest would be the worst thing for a horse with DSLD.