Situation:
A husband and wife. The husband worked for the US government for 30 years, earning a full government pension. He then worked in the private sector for 15 years, accumulating some social security benefits. His wife was a homemaker and never earned income.
Upon retirement, the husband elected to have his government pension pay out as a single life benefit. That amount offsets his social security benefit (due to the 2/3rds rule) fully during his lifetime.

Question:
Upon his passing, will his wife be eligible to receive the survivor income benefit or will she be ineligible due to his pension (even though she will not see a dime from the pension)?