I think you got closest to what I was asking, but not quite.
I did not mean to ask "if work can be submitted twice" as you say.
When mining directly / solo mining, I assume you still get rewarded for solving part of the chain, however, most solo mining nodes (including this one) do not relay those minute rewards (if any), only IF you solve the entire block. So that was the crust of my question, can a solo mining pool be set up whereby rather than (realistically) mining for nothing short of hitting the jackpot, the mining can be rewarded however lowly?
Thanks for explaining, and I am sure I am missing something that is obvious to yourself (but ofcourse very foreign to me!).
In a normal pool, when a block is found, the reward for that block is distributed to all the users who contributed work to the pool.
When solo mining, the solo miner takes the whole block reward for himself.
You cannot simultaneously give all 25 BTC to the miner that found it AND divide it up among everyone who is hashing on the pool.