I assume that when I sent BTC to an exchange and do nothing with it, the BTC doesn't just sit there doing nothing. I assume the balance is associated to my account but the BTC is pooled and stuff happens to it. Then when I withdraw my balance BTC gets sent to me form whatever is available in the exchange's system. So sort of like a bank rather than a deposit box?
If my assumption is correct then the lack of dead end could indicate it is in an exchange somewhere. Is there anything associated to transactions (familiar IP addresses etc.) that would indicate which exchange? Even if I've been ripped off, or an exchange has gone under, etc. I'd still want to know where they went rather than not knowing exactly for which reason I should be kicking myself .