Just to let you know, you are not alone in this situation, there are about five million widows and widowers receiving monthly Social Security benefits based on their deceased spouse's earnings record
Will your wife be relying on benefits based on your earnings should you pass away before her?
Yes, she would
What happens if my spouse remarries? If their future spouse is a Social Security beneficiary and the amount they receive  is more than the widow's benefit on my record, what happens?