Just as the title implies, whenever a fake player dies while containing experience points, it will drop the experience (as expected) but will still have that experience when respawned via /player. To put it another way, fake players dupe XP when killed repeatedly.

https://www.youtube.com/watch?v=K0Dikci5CZk (example recording)

Keep inventory was turned off, and there weren't other datapacks/command-blocks running which could affect player experience levels.
I am in minecraft version 1.20.1 using Carpet v1.4.112