I had 2FA enabled, I provided them with the verification they asked for. IP address, log in, last 3 transactions, and so on. The hackers requested the 2FA to be removed which I was on line when it happen (I was logged in) and booted off line. I contacted BTCe right then and my account was locked, They change the password and too contol of the email, I had to regain access. The password to account was not hacked, just my email was. And yes I had the 2FA enabled. I am not blaming the exchange AND I provided them the correct answers to their questions such as IP address and what not. I needed to change my email address, so yes with that said they know I am the owner and not helping. Hacking is not careless it means hacked.
I am not talking about the 2FA on your btc-e account. I talk about your email. Have you got 2FA on your email?
Because If you say "yes" you simply lie.
Nobody can hack a 2FA enabled email address unless they trick the owner to remove it by his own will. (I read it somewhere that there is an ongoing fraud by using google voice and trick the owner into typing a code to remove his email's 2FA) If that was your case, that's not a hack, that's being dumb.