Not affiliated with the government
I see no evidence of the chance to increase SSI benefits based on the death of a spouse.
As far as Social Security survivor benefits, in general, you cannot receive survivors benefits if you remarry before the age of 60 unless the latter marriage ends, whether by death, divorce, or annulment.
It may be possible for your unmarried child, if under age 19, to receive survivor benefits based on you ex-spouse's work record.
See here for details : http://www.ssa.gov/ww&os2.htm
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