Each miner connected to the pool will repeatedly ask for a chunk of work from the server. The work provided is a much less difficult piece of work, which results in the miner being able to submit "shares" at a relatively quick pace (in comparison to the time it would take to solve a block solo).
Each share could potentially be the answer for the block the pool is working on, and if it is, the pool solves the block and each user gets paid based on the method the pool is using to value shares. Less any required fees or donation rates.
That is not feasible because the block that you are solving for the pool includes the transaction that pays the 50BTC to the pool's account, not yours.