The Catechism of the Catholic Church (CCC, no. 1030) tells us authoritatively that such souls must "achieve the holiness necessary to enter the joy of heaven.", and "after death...undergo purification" Though the situation of the souls after death is already determined by God at the moment of death, we can yet assist them by offering prayers, good works, sufferings and sacrifices on thier behalf. It is not only a good thing to do, it is verily our duty to assist them. I offer this novena prayer for your use so that they may be aided.
Novena on Behalf of the Holy Souls of Purgatory
O Lord God almighty I pray Thee,
by the precious blood which Thy Divine Son Jesus
shed in the garden,
deliver the souls in Purgatory,
and especially that soul amongst them all
which is most destitute of spiritual aid;
and vouchsafe to bring it to Thy glory,
there to praise and bless Thee forever.
Our Father, Hail Mary
Out of the depths I have cried to Thee, O Lord
Lord hear my voice.
Let Thine ears be attentive: to the voice of my supplication.
If Thou, O Lord, wilt mark iniquities
Lord who shall stand it?
For with Thee there is merciful forgiveness: and by reason of Thy law
I have waited for Thee O Lord.
My soul hath relied on His word: my soul hath hoped in the Lord.
From the morning watch, even unto night
Let Israel hope in the Lord.
For with the Lord there is mercy, and with Him plentiful redemption.
And He shall redeem Israel, from all his inquities.
Eternal rest grant unto them, O Lord
And let perpetual light shine upon them
May they rest in peace.