As Kyle implies in the comments, mechanical energy is generally defined only up to a constant. Therefore, if you choose your constant as a large, negative number, you could have a total energy that is negative even with a very fast moving particle. Likewise, if you choose your potential energy to equal zero at, say, the top of a cliff, then anything you throw off the cliff will have negative potential energy once it falls below your feet.

This is not strictly a duplicate, but it is probably worthwhile to link to this answer I posted a while back.

As Kyle implies in the comments, mechanical energy is generally defined only up to a constant. Therefore, if you choose your constant as a large, negative number, you could have a total energy that is negative even with a very fast moving particle. Likewise, if you choose your potential energy to equal zero at, say, the top of a cliff, then anything you throw off the cliff will have negative potential energy once it falls below your feet.

This is not strictly a duplicate, but it is probably worthwhile to link to this answer I posted a while back.