Assume that one spouse worked and the other didn’t, they are still married and retired. As a result the spouse who didn’t work gets spousal benefits which I think are half the benefits that the wage earning spouse earned.
What happens if one dies? What happens if the wage earning spouse dies? If the wage earning spouse is earning $1600 and the non-wage earning spouse is earning $800, what happens to the non-wage earning spouse? Do they get a boost to $1600?
What if the non-wage earning spouse dies? Does the wage earning spouse stay at $1600, or what?
She no longer has a spouse, she gets survivor benefits. I recently helped a widow apply for survivor benefits. When it was approved, it replaced her previous SSI benefits. Actually she ended up losing some of her some income, since the (higher) survivor benefits put her just over the income where she now needed to pay for some insurance coverage which was formerly free.
Based on what I’ve read, the earnings after the divorce are not treated differently. One gets a benefit based on the other earners benefit. (Often your own benefit plus a matching boost to the other’s higher benefit.)
If the other person is deceased, then more rules apply.
Note in reading those links various rules about 10+ years of marriage, etc.