Like, all your PC boxes are filled, your party is filled - does it give you a choice to release one of the Pokemon in your party or somethin'?
This happened to me on Pokemon soulsilver. I was told there was no more room in the storage box and that the Pokemon broke free. You would have to have 6x Pokemon on you and the boxes full for this effect to take place. On the Pokemon x/y series however you get 30x storage boxes.... Battle box.... Poke bank..... and 6x Pokemon on trained (pokebank) holds upto 3000 Pokemon. So hopefuly that's enough Pokemon for any person. Also you could spread the Pokemon around by buying Pokemon x along with Pokemon Y and use both as storage. And even use a 2nd ds and purchase poke bank on the other one. You'd end up getting 6000 Pokemon storage and 60 boxes for use. Lots of Pokemon to store LOL.
Hope I helped!
You fail to catch any Pokemon.