There are 3 concepts you may be confused by.
1. If you receive social security, it may be taxable depending on your other income. Filing Married Filing Separately guarantees that his social security will be taxable even if it would not be taxable when filing jointly.
2. If he continues to work, he will still be subject to withholding of social security tax. That always applies to income earned from working no matter how old the worker is. However, by adding to his credits in the social security system, continuing to work may increase his benefits.
3. Below his official retirement age, working will reduce his benefit paid by social security. After his official retirement age, working does not reduce his benefit.
