From figures young enough to be called boys and girls, to the aged who look like they might breathe their last at any moment.
Literal
Boy-girl [quotative-と] should-call age [gen-の] people [from-から], soon great-passing [obj-を] accomplish [not-のではない] [quotative-という] elderly [gen-の] people [gen-の] figure [until-まで] exist.
A sweeping descriptive sentence using the ~から~まで ('from X to Y') inclusive range pattern to describe a crowd's age span. と呼ぶべき ('should be called') is the volitional/obligation べき attached to 呼ぶ, used attributively: 'those who should be called boys and girls.' 大往生を遂げる ('to accomplish a great passing') is a literary/respectful euphemism for 'to die peacefully at a ripe old age.' ~のではないかという is a complex nested structure: のでは ('probably') + ないか ('not?') + という ('called/such that'), giving 'those who one might say / those who might.' Elevated literary style.