So an example here might be that you were working for a client and work wasn't fully completed on time. You made a good faith effort to get the work done, so while the company you were working for might be entitled to compensation from your LLC they can't come after your house.
Finally, let me caveat all this by saying that the standards for "piercing the corporate veil" vary by state and as always you should consult with a lawyer before making a final determination. Also, another work around is to form a multi-member LLC and hold formal annual meetings. This is normally enough for most states to consider the LLC as a separate distinct entity and prevent piercing of the corporate veil.