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According to SSA, unmarried children who are under 18 (up to age 19 if attending elementary or secondary school full time) can be eligible to receive Social Security benefits when a parent dies.
The child can get benefits at any age if he or she was disabled before age 22 and remains disabled.
A child under age 18 or disabled may receive up to 75 percent of the parent's available payment.
How much the child can receive would depend on the parent's average lifetime earnings. The higher the earnings were, the higher the benefits would be. SSA calculates a basic amount as if the parent had reached full retirement age at the time they passed away.
If your wife did not work there would be no earnings to calculate a benefit on unfortunately.