Players at very high Y levels cannot move vertically

Partially relates to MC-227347.
The security level is Private due to reproduction steps that should potentially be kept private.

The bug

At very high Y levels, the player cannot move vertically.

This video (flashing lights warning!) demonstrates this. When using the elytra, one would expect the player to slowly fall, but this is not the case. The player remains at the same level as the pigs.

How to reproduce

1. Summon a pig
2. Put a saddle on the pig
3. Start riding the pig
4. Use the following command (note that the y-value given is completely random, and can probably be less than this):

   /data merge entity @e[type=pig,limit=1,sort=nearest] {Pos:[0.0,17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592.0,0.0]}

5. Dismount the pig
6. Try to move up or down
   You are unable to do this