How does grief from a death in the family affect a child's social development?

Lots of variables: Your excellent question is hard to answer, because it depends on who died, age of child, effect on rest of family, and many other variables. Research shows that children who lose their mother before age 11 are at increased risk of depression as adults, but there are many possible explanations. Broadly, helping children grieve in age-appropriate ways is best way to minimize lasting impairment.

Age-dependent: A young child mirrors the reactions of the family. Keep routines as normal as possible. Children understand the finality of death around age 10. Withdrawal, loss of interest in usual activities and friends, changes in eating/sleeping and irritability are signs of depression. Seek help from a child psychologist if concerned.