I'm confused. Please help me underestand. Other posters have stated that while forgiveness for sins was obtained by Jesus on the cross, there remains the issue of suffering for those sins- the suffering that the believer has not yet "paid" on earth. The suffering produces cleansing. Correct?
How then are your prayers "paying the debt" of someone else? Are your prayers causing them to suffer more? And if you're praying to God to "pour out His Grace" on the suffering individual, what exactly are you asking God to do? Make him suffer more or less? And how does Grace fit into this? Grace is an unmerited gift. It seems that purgatory, however, is the paying of a debt- a debt that you say has to be paid in full BY THE INDIVIDUAL. This gets to the heart of the difference between RC's and Protestants. We agree the debt has to be paid in full- but we believe the God paid the debt in full- there's nothing left for the individual to do, which is a good thing, since there is nothing the individual CAN do!
I think there is some confusion here (understatement of the day). Here is my understanding [by no means do I claim to be giving the official teaching of the Catholic Church, and I would submit my opinion to the Magesterium if it is wrong].
Christ did die for our sins. He earned infinite grace, which he provides freely to us sinners here below. But, we have to comply with the grace to receive it. That is, we are free to accept or reject it. When we sin, we are rejecting God's grace. When we act in conformity to the will of God, we become a "channel" for that grace, so to speak, and because God loves us and wants us to be happy with him in heaven, He will continue to provide more and more grace to the soul who does not impede this.
One way to act in conformity with the will of God is to unite our suffering to Him instead of complaining or being bitter. When we suffer well and offer this to God as our minor "participation" in His suffering on the cross, we are given more grace, because we are acting in conformity with the will of God. Another way is through prayer, where we unite our heart and mind to God, and He pours out grace to that soul for conforming with His will.
As I stated above, when we sin we reject God's grace. It leaves a "blemish" on our soul, so to speak. These blemishes can be washed clean by the grace of God, which can be "earned" simply by complying with the grace that God is freely giving.
To enter into heaven a soul must be in a state of perfection. That is, none of these blemishes from sin can remain. Therefore the soul enters Purgatory, where the suffering soul complies with the grace of God until it has received sufficient grace to be in a state of perfection.
I don't believe it has ever been declared what sort of "suffering" the souls in Purgatory undergo. Some hold that it is simply a loss of the beatific vision, some hold that it is somewhat similar to the fires of hell. One of the more widely held beliefs is that it is catered to the sorts of sins which were not overcome while on earth. Those of a more serious nature are going to be given a more serious purgation.
Now, how this all fits to praying for the souls in Purgatory. I can offer prayers to God, and ask that He bestow the grace which I would receive to the soul(s) in Purgatory. If that is in conformity with His will, He will do so, and the amount of "suffering" a soul will have to do will be lessened, because I am channeling my grace to that soul.
Thus, your statement that the "debt must be paid in full by the individual", I would have to say is incorrect. The debt is paid by the grace freely given by God, but if we don't allow Him to pay the whole thing by not conforming to His will while on earth, then the debt remains outstanding until we do accept that grace.