and so if somebody steals your coins, you might still have them also. there could be multiple copies of the same wallet. they haven't vanished from your harddrive. just a copy-and-paste operation .
And so, is the wallet smart enough to realize this? is the online exchange smart enough to realize this? in real time - not 3 months later when you attempt to spend the coins, and find out they are invalid now.
Ok ..I think I understand what you're saying. Yes, your wallet is only code that can be copied. Someone that has obtained a copy of your wallet can either import it into their client and withdraw the funds immediately, ...or, they could sit on it and wait and watch for the balance to increase. Ultimately, once some has your wallet dat file, that particular wallet is forever compromised even if you're unaware of it. At the very time the thief withdraws the funds from your wallet balance, the shown balance in YOUR client will reflect that right away once it reconciles itself against the blockchain. You may be oblivious to your wallet file being stolen, but once the coins are spent, you will be aware.
As far as an online exchange goes, as mentioned previously, your coins are really in the exchange's coin pool. If someone gets access directly to your account you would most likely notice that your coins were stolen the next time you log into your account and notice a missing balance. If the exchange is hacked, well you could know immediately, or it could be some time depending upon the action taken by the exchange.