Losses when trading with bitcoins
Yes, absolutely. Here's just one example of how this can happen:


You invest Bitcoins worth $100 in some kind of high interest scheme.
You cash out of the scheme and get Bitcoins worth $200.
You invest those Bitcoins.
You lose them.
The high interest scheme turns out to be a Ponzi scheme. You are sued to clawback the $100 value of the Bitcoins that were fraudulently paid to you.
You lose that suit and now owe $100 on top of the $100 you invested.


Another example would be if you unknowingly withdraw funds from an exchange that's insolvent, then reinvest and lose those funds. If the exchange declares bankruptcy, your withdrawal could be ruled a preferential transfer and you would have to repay it.