“Catholics seem to believe that, if a person did not accept Christ as the Savior, they get a second chance to be purged of their sins, but I’m not aware of any Biblical references other than some folks interpretations to indicate a second chance”
Purgatory is not a second chance. If you make it to purgatory you are on your way to heaven. You have already known Jesus as your Savior. On the other hand, if you die in mortal sin you’re going to hell.
Purgatory is a place of final cleansing of temporal punishment for sins which have already been repented of and forgiven.
Example (a pretty lame one that has been around for a while but might help)
You’re a kid playing baseball in the street. You accidentally break a neighbor’s window. You apologize. The neighbor forgives you. You are still obligated to pay for the broken window.
That’s purgatory.
I guess my question is, why did Jesus pay the price for our sins with His blood? Why did the prophet Jeremiah talk about the New Covenant by saying that God would forgive our wickedness and recognize our sins no more? Your explanation almost sounds like Purgatory is a reincarnation where you get to atone for the sins that Jesus died for - what makes you think that souls in Purgatory would be any more likely to atone/pay for any "outstanding" sins that somehow didn't get paid for with the Blood of the Savior?
That's one of the main reasons I decided to get out of religion and stick with Biblical Truth vs. dealing with all these hokey "between the lines" deals that the mortal men who made up the religion decided should be looked at as truths. There's over 30,000 sects of Christianity and they all claim the same Savior, but every one has different reads on parts of the Bible.