Can a miner not find a share in his work unit? I understand that a mining pool operator distribute work units at it miners.

Is it possible that a miner can find no share in his work unit?

If is the case, this mean a miner can work for nothing?
A good pool should manage difficulty levels so that every qualified
1 worker finds at least some share.  It may be a very small share, but something should be counted.

1 By qualified, I mean a processor in the same league as the rest of the pool.  If you join an Intel CPU miner to a pool of ASIC miners, your miner would not be qualified, and it would be appropriate to not get any shares.