Why not 'old ladies' as the last word was 'them'.

If one old lady fell, the sentence should end with 'her':

The passer-by saw the old lady fall but he did not stop to help her.

If more than one old lady fell, the sentence should end with 'them':

The passer-by saw the old ladies fall but he did not stop to help them.

Note: of relevance to this topic is the 'singular they' (or them). When the sex of a person is not stated, one can use 'they' or 'them'. This may be preferable to 'he or she' or 'him or her'.

A cruel passer-by is one who sees an old person fall but does not stop to help them.

This is equivalent to: "A cruel passer-by is one who sees an old person fall but does not stop to help him or her. "

This is intentional dumbing down. The media who have appointed themselves role models for language usage go out of their way to change the antecedent to the singular just so they can use an illogical plural. Besides, "he" is the traditional shorthand for "he or she." It basically means "this person" and is related to "here," which means "this place."
No one can honestly object to "he" for "he or she" and put "they" in its place. The English language regularly changes according to number but rarely according to gender.

The passer-by saw the old sage fall but he did not stop to help.

I agree.
"Intentional" 'dumbing-down'?

The singular they has not only been widely used by good writers for centuries, but is now generally accepted, except by some conservative grammarians. It had emerged by the 14th century and is common in everyday spoken English, but its use has been the target of criticism since the late 19th century. Its use in formal English has increased with the trend toward gender-inclusive language. The prescription of the generic 'he' is a comparatively recent thing (again late 19th C.).

Don't trust these New Grammar snakes. They also spell *mike* "mic" just to prove how much mind control they have. They're thinking "Let's make up the most absurd and unphonetic spelling we can. If our viewers blindly obey such stupidity, we really have power over them."

IF YOU'VE HEARD OF SOMEONE, DON'T LISTEN TO HIM

Such things can be refuted by what else they lead to, such as when the gender of the singular is known by the speaker but the plural pronoun is still used: "I met someone who was there and they said..." "The usher is here and they say I can't talk on my phone."

We should not respect the authority of no-talent classclimbers who brownnose their way into positions high enough to influence everybody's grammar. This proves we have inferior people in superior positions rather than that we should follow their lead because of the conformist feeling that they must be superior if they reached those positions.

They act as if, when a boss gives a receptionist a package and says, "If someone from headquarters shows up, give him this," and a woman shows up from there, she wouldn't hand the package over. Yet they'd never imagine, equally logical, that if the boss had said, "Give them this," she wouldn't hand it over if only one person showed up.

"Mic", as used in broadcasting, etc is simply the first 3 letters of 'microphone', and has been around since at least the early 1950s. Sage of Main Street? Crank of Nut Street more like.

By the same token, the on-air airheads should spell Mike "Mich" and bike "bic." You must know people in the business and want to defend their inferiority. Hiring people like that has dragged down America in all sectors. People with such learning disabilities have no right to their jobs. College graduates display a 6th Grader's knowledge of English, because college is for low-talent class-climbers who are willing to live like teenagers there because they are afraid to grow up. Making up their own silly phonics shows how conceited such immature frauds are.

Sage of main street, you come over like a monomaniac. Half the things you identify as modern abominations are actually legitimate variants with very long and respectable pedigrees.