Quote of comment by [Mojang] Georgii Gavrichev from a private report about this:
The chunks that are regenerated have the flag "LightPopulated" set to false, which normally can only happen to the chunks on the border of the world, so the upgrade process drops them (since they might have not generated fully). This is a reasonable behavior, since those chunks couldn't've been modified by the player. Our guess is that you used some kind of a tool to edit the chunks; if so, please set that flag to true, and it should fix this issue for you.
If your server is/was a Spigot server you will need to use CraftBukkit/Spigot to convert the world. Spigot in 1.12 didn't set the "LightPopulated" flag, so that vanilla Minecraft will reset those chunks.
After a conversion with Spigot 1.13 the world can be opened in vanilla Minecraft again without problems.
See also the Bukkit, CraftBukkit, Spigot & BungeeCord 1.13 release notes:
+++ Spigot 1.12.2 worlds must be converted using CraftBukkit/Spigot and NOT Vanilla.
When i migrated my island world from 1.12 to 1.13, i have only 1/4 island. Around is new generated world.
1.12 world download - https://mega.nz/#F!C3g3kKwK!VjHjeZ9cHEDmWBikp6rwyg
World location - /tp -1536 80 1536
Images - https://imgur.com/a/KI70rz5