You’re not getting something for nothing—you’re paying for the policy.
For term life insurance you have to keep the policy in force by paying your monthly or annual payment during the term you selected, which may be 10, 15, 20 or 30 years of coverage. Then if you die during the period that the policy is in effect your beneficiary would receive the face amount of the policy. Learn the basics of term life insurance here.
The only time you could “owe money” to your life insurance policy is if you have a whole life policy and borrowed against it by withdrawing some or all of its cash value. However, if you borrowed against it and then died, your wife wouldn’t actually owe money but instead the life insurance policy payout would be reduced by the amount you borrowed and didn’t pay back in.