Purgatorial punishment is a position held by some Universalists. Purgatory is primarily Roman Catholic doctrine where the souls of those who have died go to a place for purification via temporal punishment. After an appropriate period of time, they are released and go be with God. Likewise in the universalistic purgatorial teaching, again which is not held by all Universalists, after a person has suffered the punishment due to his sins, he is released from that punishment and is allowed to join the presence of God.
Besides being unbiblical, there's also a logical problem.
First of all, the Bible does not teach purgatory. It teaches justification by faith alone in Christ alone (Romans 3:28; 4:1-5; 5:1; Ephesians 2:8-9). There is no need for suffering after our earthly lives in order to be made "worthy" in any sense to be with God. Our worthiness is completely embedded in the work of Christ on the cross.
Second, in universalistic purgatorial punishment, the suffering any individual must undergo in the afterlife must be in accordance to the sins he has committed. Sin is breaking the law of God (1 John 3:4). If a Universalist says that a person must suffer for a period of time before being released, he is saying that the punishment is due to the requirements of the law. But this would mean that a person is saved from eternal punishment by undergoing a temporal punishment. In other words, it is a form of salvation by compliance with the law. This is, of course, not biblical and false.
Now the Universalist may respond that the punishment is indeed suffered and he is not saved from it. He must undergo that punishment before he can be in God's presence. But this presupposes the idea that human suffering is capable of appeasing God. If that were the case, Christ did not need to come and die on the cross for us.
"I do not nullify the grace of God, for if righteousness comes through the Law, then Christ died needlessly," (Galatians 2:21).