An old unconnected htc one x+ recently stolen The phone wasn't connected to my network,  I was just using it for music. But, if connected through wifi, I was able to go online. My phone company is aware of the theft and red flagged it.
 Can these theives still break into my accts and find info on me?  Can they assume my identity and request password resets to get into my accounts?
The short answer is... maybe.  Did you have a pin or pattern set on your phone to prevent anyone from opening it?  If you had something as simple as a pattern lockscreen or a 4 digit pin, it's highly unlikely (although, not at all impossible) that anyone is going to invest the time and effort it would take to break that security.  If you left it wide open with no sort of lockscreen protection, then anything you have saved on that phone is open game.  If you saved logins through apps on your phone... all they would have to do is connect to wifi and have access to whatever apps you have saved logins enabled for.  Your google account, at the very least, could be compromised easily (since they already have access to it- I feel certain if you're worried about this then you dont have 2FA enabled). I would recommend changing password to any services you used on that phone as a precaution, especially if you didn't have a lock feature enabled.