I just finished reading This Is the Way the World Ends by James Morrow.
The last woman on Earth lived in the Bahamas, was beautiful and intelligent. Due to radioactive fallout, all of her children had been stillborn.
After a month of living alone, she hung herself.
The last man on Earth was taken to Antarctica by "those who were "unadmitted" into life.
I would tell you what he did, whether he restarted the human race or not, but that would be giving away the ending to a very good book.
Suffice to say that since humans are social creatures, I highly doubt most of us would get along very long alone.