Okay, that seems unfair to me, that is, if I lasted with my wife for 9 years and 11 months, would social security really help my family if I died?
Yes, if you earn enough social security credits then Social Security would help your survivors with the benefits you earn while working.
Could my widow apply for disability benefits after my death?
She would need to contact Social Security at 1-800-772-1213 . The process could get faster if she completes an Adult Disability Report before her appointment.