Is it possible to track a switched off mobile device?
for you? nope.
but for government/mobile carrier? not impossible.
Some phones did/do have special tracking chips that allow sending commands to a "switched off" device (it's still keeping the mobile network barely powered), haven't heard of those used outside of u.s.a. though.
there's an easy solution, use only phones with removable batteries, and remove the battery after shutting down normally, if you're really paranoid then even wrap the phone in tin foil or such...(because they might have a secret tiny battery that lasts for hour(s) hidden somewhere, you never know)
oh, and if someone is claiming to hack into your phone and track you (unless you do X), they're most probably just bluffing...