Last month I kegged a Belgian Dubbel. It sat in the keg laggering for a little over a month. Then I pulled about 10-12 glasses from it for immediate consumption. The beer tastes great and, after the first 1 or two, was very clear.
Then I bottled the rest directly from the keg. After the bottles sat for an hour or two, I saw a layer of sediment in all of the bottles.
The keg had not moved the slightest bit in over a month, including during bottling. I did not add anything post fermentation (extra yeast, dry hops, etc...), all bottles were clean.
The sediment was in all bottles, not the first few, not most. Every bottle has (approximately) the same amount of sediment.
It appears as if something in the beer changed density after being in the bottle and settled out.