Some years back, I read somewhere that when ever anyone falls from a state of grace, God more or less immediately raises someone else up to a state of grace to take their place.

Is this accurate, and where can I find this teaching?

On the contrary, The Lord says of the saints that, "they will be as the angels of God" (Mt. 22:30).

I answer that, As above explained (a. 4 & 7), the orders of the angels are distinguished according to the conditions of nature and according to the gifts of grace. Considered only as regards the grade of nature, men can in no way be assumed into the angelic orders; for the natural distinction will always remain. In view of this distinction, some asserted that men can in no way be transferred to an equality with the angels; but this is erroneous, contradicting as it does the promise of Christ saying that the children of the resurrection will be equal to the angels in heaven (Lk. 20:36). For whatever belongs to nature is the material part of an order; whilst that which perfects is from grace which depends on the liberality of God, and not on the order of nature. Therefore by the gift of grace men can merit glory in such a degree as to be equal to the angels, in each of the angelic grades; and this implies that men are taken up into the orders of the angels. Some, however, say that not all who are saved are assumed into the angelic orders, but only virgins or the perfect; and that the other will constitute their own order, as it were, corresponding to the whole society of the angels. But this is against what Augustine says (De Civ. Dei xii, 9), that "there will not be two societies of men and angels, but only one; because the beatitude of all is to cleave to God alone." -Summa Theologica I q. 108 a. 8,