Do Those Who Died Prior to Jesus's Coming Get a Second Chance to be Saved?

According to Paul, people of faith who died without first receiving "the things promised" will still be welcomed into Heaven. However, these people were already people of faith when they died. Therefore, they need no second chance. He writes,  

"All these people were still living by faith when they died. They did not receive the things promised; they only saw them and welcomed them from a distance, admitting that they were foreigners and strangers on earth. People who say such things show that they are looking for a country of their own. If they had been thinking of the country they had left, they would have had opportunity to return. Instead, they were longing for a better country—a heavenly one. Therefore God is not ashamed to be called their God, for he has prepared a city for them... These were all commended for their faith, yet none of them received what had been promised, since God had planned something better for us so that only together with us would they be made perfect." (Hebrews 11:13-16, 39-40, emphasis added). 

Therefore, no, those who died prior to Christ will not be given a second chance. As Paul explained earlier in Hebrews, people will "die once" and after that "face judgment" (9:27). But they don't need a second chance. By remaining in faith in the true God and looking forward in hope to His glorious Savior, the Messiah, until their deaths, they will be saved and welcomed into Heaven.