Normally, the part of the health insurance premium that you contributed is added to the employer's contribution to the same and is reported in box 12 with a code of DD. Yes, these amounts are pre-tax.
Box 11 is rarely used - "Report distributions to an employee from a nonqualified plan or nongovernmental section 457(b) plan in box 11. " (from the IRS instructions). This "probably" has nothing to do with your health insurance premiums. I also don't know why it would be negative.
You need to ask your employer about why your W-2 is completed the way it is.
