If the game is saved with the player standing on top of a chest, reopening that world spawns the player in the chest (i.e. both player and chest are standing on the same block in the same space).
This happens with both single and double chests, and the player only goes through 1 chest-height total (saving and quitting while mid-way through a chest does not spawn the player one block lower to the chest below).
There are no issues with this bug other than the minor annoyance which is easily solved by walking straight out (not into connected chests) or jumping.
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This issue is now being tracked at MCPE-84023.
Affects "1.14.20" and "1.16.201 Hotfix" as well (tested only those versions on Android). Video (1.16.201 Hotfix)