On his website, Arminian Perspectives, Ben Henshaw has a questions page at which he answers questions about Arminianism and Calvinism that visitors to his site pose in the comment section of the page. The following is a question and answer interaction between Ben and a commenter named Phileo:
Question: If Jesus made atonement for all sins (He died for all sins) doesn’t that mean that some sins (sins that are not forgiven) are paid for twice once by the death of Jesus and second by the death of the sinner?
The short answer is that the atonement is both provisional and conditionally applied. Christ made satisfaction for sins, but only those who come to be in union with Him through faith benefit from that satisfaction. Double payment would only follow if the atonement was unconditionally applied.
F. Leroy Forlines writes,
“The Scriptural evidence is clear that it is through union with Christ that the benefits of Christ’s atonement, by which we are justified, are applied to us: ‘Likewise reckon ye also yourselves to be dead indeed to sin, but alive to God through Christ Jesus our Lord’ (Rom. 6:11). ‘Through’ in this verse translates the Greek preposition en. It is better to translate it ‘in.’ It is ‘in Christ Jesus’ that we are to consider ourselves to be dead to sin and alive to God. Again Paul says, ‘There is no condemnation to them which are in Christ Jesus’ (Rom. 8:1). The grounds for ‘no condemnation’ is being ‘in Christ Jesus’“ (The Quest For Truth, 192- emphasis his).
“Prior to union with Christ on the condition of faith, a person could not say, ‘I died with Christ.’ Immediately, upon union with Christ a person can say, ‘I died with Christ.’ The history of the cross became his history, not in the experiential sense, but by identification so that he received full credit for that death….On the condition of faith, we are placed in union with Christ. Based on that union we receive His death and righteousness. Based on the fact that Christ’s death and righteousness became our death and righteousness, God as judge declares us righteous….atonement is provisionary until the time it is applied. The only way to deny the provisionary nature of the atonement is to consider all people for whom Christ died to be justified before they experience faith. Once it is accepted that atonement is provisionary, the objection, which states that penal satisfaction leads to either universalism or limited atonement, is seen to be invalid. Atonement is provisionary until it is applied. It can be applied only on the condition of faith and on the grounds of union with Christ. When applied, atonement becomes efficacious. Then and only then is atonement efficacious. The objection that the penal satisfaction view requires either universalism or limited atonement fails…The discussion above about provisionary atonement and union with Christ answers the objection [of double payment]. The death of Christ is not on the sinner’s account who goes to Hell. His account does not show a double payment. It is true that his sins were paid for provisionally, but there is no double payment as long as there is no double entry on the person’s account. No person will go to Hell with the death and righteousness of Christ on his account” (194, 196, 207- emphasis his).
For more on this, you may want to read the following posts: