Once i tried to open my world and got error "You are out of data storage space and minecraft is unable to save your progress! Minecraft will return you to the Main Menu to clear up storage space" and after 2nd attempt i got "there was a problem loading this world", but my world weights only 75.8 MB and i have about 60 GB free space on my hard drive.
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Many communities are experiencing this same issue. The host will see an error indicating it is our of space, and players will see an error saying the world is corrupt.
The community seems to be in agreement that it is related to loading new chunks, which is why it happens most often while traveling long distances, like with a boat.
There is already a bug report higher up in the priority list(90 Votes+). You can help draw some attention to our problem by voting for it & adding any additional details you may have. Hopefully by consolidating and raising awareness of the one issue we all will receive a faster resolution.
https://bugs.mojang.com/browse/MCPE-32501