If you tap on a Pokemon and then it despawns for everyone then you throw a Pokeball at it and it happens to break out, and then runs away; does it run because it despawned for everyone or just a coincidence? This has happened to me a few times and id like to know if this is the reason. Can someone please test this? Or is that asking too much?
The only way to test this is to have a friend with you and use pokevision.com which will tell you when they despawn. Find a Pokemon that is close to despawning and wait until the last 10 seconds or whatever before one of you tap it and the other sees it despawn, then throw a bad throw on it and if it breaks out and runs away you will know that this theory is correct.
Best Answer
I have tested this on numerous high-level Pokemon, since nobody cares about a mid-200's Pidgey.
With Pokevision up, I clicked on a Pokemon and then waited until it "despawned" from Pokevision. I then proceeded to throw standard Pokeballs. After breaking free, the Pokemon did not run away.