What's an example of an ExtraNonce2 value that would be considered invalid? I've been learning about mining as part of a pool and using the Stratum protocol to submit completed work back to a pool -- https://en.bitcoin.it/wiki/Stratum_mining_protocol .  There is this parameter, "ExtraNonce2," a value that the miner keeps changing.  Could someone tell me a scenario where a pool worker submits a nonce that correctly hashes the data it was given according to the difficulty, but it submits an "ExtraNonce2" value that causes the mining pool to reject the submission?
There is no such a scenario. The ExtraNonce2 is part of the data that is hashed. So if a miner finds a valid nonce, he must also have the corresponding ExtraNonce2 that is part of the data that is hashed in order to produce a valid block hash.