Do unmarried women become public property?

In a lecture video available on YouTube (and in many more) Dr. Zakir Naik claimed that unmarried women become public property. My questions - 1) Does Islam support this statement? Are there any verses in Quran or Hadith regarding this? If yes to the above questions then, 2) What is the upper age limit for a woman to get married? Because a woman unmarried now may be married tomorrow, so when she could be public property?