The answer, unfortunately, is "it depends."
In general, debts incurred before marriage are "separate property" debts, which means that the spouse of the debtor is not liable. However, if you own assets at your death, those assets will need to be used to satisfy any of your separate property debt. Normally, this would be handled through a probate unless your assets are held in a trust (in which case the trust assets could be sold to pay off the debts).
If you wanted to avoid this result, you could transfer all of your assets to your wife. However, you should check with an attorney about fraudulent transfer rules before trying this.