I don't know exactly what your saying, but I think I get the gist.
When you transfer a Pokemon from any generation to another, you cannot get that Pokemon back. It will remain in your Pokedex, (it was captured at some point,) but it's not in your boxes or your party.
Yes, when you transfer a legendary, starter, or something that's only obtainable once, it cannot be recaptured in your game.
If what Fizz said is how you are thinking, then no, there is no "recapturing" similar to Pal Park or the mini game when transferring to Bank. As soon as you transfer, the Pokemon are immediately deposited in the Transport Box of Pokemon Bank, where you can move them directly into your Gen 6 or 7 games.
Once a Pokemon is in Pokemon Bank, it can not be sent back to a Generation 4 or 5 game, so no, you would not be able to get your Pokemon back to Pokemon White. You can also not send Pokemon directly from Gen 4 to Pokemon Bank, you have to send them to a Gen 5 game first. You can transfer whatever Pokemon you want, but, for example if you transfer a legendary, you will not be able to re-catch that Pokemon in the original game.
If you have any more questions please ask.
