What factors contribute to the lower financial status of older women compared to that of older men? ?

If she was working legally she paid into SS.

If you mean she was a stay at home Mom she gets SS benefits based on her husband's earnings.  If she was a stay at home Mom who is now a 70 year old widow she would draw survivors benefits which would equal what her husband's was.

She would have Social Security benefits as her employers would have been responsible for deducting them from wages.

The woman took the alimony from her two ex’s and bought slum apartment buildings where the old man is spending most of his social security.

The only way she wouldn't have SS benefits is if she never reported her income.

If she didn't report her income, she might have more money because she never paid taxes. 

The woman who worked privately should have earned SS benefits if her employer was paying her correctly. If she worked under the table so doesn't qualify, she's done it to herself. Tax evasion comes with a whole host of problems.  Housework and childcare is generally low-paying, so she wouldn't have earned much in benefits. She would have had to save substantial amounts from her salary in order to retire, or have a very generous employer.