It was many years after Thrain had left his people that I found him, and he had then been in the pits of Dol Guldur for five years at least. I do not know how he endured for so long, nor how he kept these things [i.e. the map and key to the secret door in the Lonely Mountain] hidden through all his torments. I think that the Dark Power had desired nothing from him except the Ring only, and when he had taken that he troubled no further, but just flung the broken prisoner into the pits to rave until he died. A small oversight; but it proved fatal. Small oversights often do.
From Unfinished Tales by JRR Tolkien (1980): Gandalf is here describing how he came by the map and key which led to Thorin's expedition to the Lonely Mountain; which led to the death of Smaug and founding a new kingdom of Esgaroth; and the finding of the One Ring by Bilbo; which prevented Sauron from allying with Smaug to destroy Lothlorien and Rivendell; and led to the destruction of the One Ring and the saving of Middle Earth.
This is - of course - how Jesus told us all to live in the Gospels ("consider the lilies" etc) - which is not to ignore the future, nor to live unthinkingly or in denial of reality; but to do the right things (one at a time, as they arise and not because they are part of a strategy) and trust to God to organize matters for the best.
God does this positively, and negatively.
Positively by weaving-together the work of all Men who do good (and doing includes thinking).
Such positive divine providence is shown at work in The Lord of the Rings where the free choices of the characters lead to positive unforeseen (and unforeseeable - even by the wisest such as Gandalf, Elrond and Galadriel) outcomes.
For instance the quest of Frodo was not a plan. Other than that he was to seek destruction of the One Ring in the cracks of doom; Frodo had no idea how that could or should be accomplished.
For instance, there was no plan about how to get into Mordor. Frodo simply took things one step at a time, and tried to make the right choice at each step; sustained at first by hope and later by duty (and relying on Sam's hope). Finally the destruction was accomplished only by the turning of evil against itself - when Gollum did what Frodo could not.
All through the story, there are many examples of characters who need to discover what is destined, or divinely intended; and then to choose whether (or not) to make that choice. Frodo must choose to bear the ring, choose not to use it (albeit he fails, twice - at Bree and on Weathertop), choose not to use its invisibility to escape the Barrow Wight and abandon his friends (he resisted this temptation) and so forth.
Divine destiny or providence is able to use these right choices to weave-together a sequence of events that eventually leads - by paths completely unforeseen and indeed impossible to foresee - to the triumph of the forces of Good, on the side of God.
The failures of choice need not be fatal to good outcomes but they do seem to lead to suboptimal outcomes; for instance to greater suffering than would otherwise (probably) have been the case. Frodo's use of the ring in Bree led to the attack on the Prancing Pony, loss of the ponies and the chance of slipping away unseen; at Weathertop the ring seems to have allowed the Witch King to stab Frodo with a Morgul knife, which gave him permanent pain afterwards.
But there are also many examples of 'negative providence' where the side of evil makes mistakes - sometimes apparently small mistakes (those "small oversights") which are taken-up, wedged-open, and then in many ways used by God to lead to the downfall of evil.
A basic plot point is that Sauron repeatedly makes 'small' oversights of neglecting the (to him) small threats - such as disregarding Hobbits; seeing them as trivial: unimportant to his grand plans and schemes.
Sauron's eye is focused upon the Great Powers, especially the fake threat that Aragorn - heir of Isildur - had taken the ring; so Sauron neglected to watch his borders.
Even when a hobbit (Frodo) was taken prisoner in Cirith Ungol, Sauron's attention (and that of his servants) was diverted elsewhere to the ongoing war. The orcs squabbled and killed each other; Frodo was released by Sam; and the two of them (and Gollum, trailing) were able to cross Mordor undetected and unmolested. "A small oversight; but it proved fatal."
"Oft evil will shall evil mar" says Theoden; and more generally this is seen in that the essential nature of evil creates blind-spots that lead inevitably to oversights - sometimes small, sometimes large.
Thus, even in a world dominated by evil, God can work good by-means-of the oversights of evil.
Even a 'small' oversight may be expanded by divine providence; much as a wedge may expand a tiny crack to break a rock... The very strength and rigidity of the rock works against itself - so that the whole rock splits apart instead of crumbling at the pressure point.
Christians in these End Times - who are inhabiting a world of corrupt people led by a totalitarian global 'government' operating in obedience to Satan and in accordance with an inverted value system - may find great encouragement in such possibilities.
So long as there are some men who make good choices - some Men who have chosen to ally with the side of God, Good and Divine Creation; then providence will be continually be weaving-together their many small and specific good intentions and acts into large (but mostly invisible) sequences.
Not according to a plan, but according to intention. Continually updating means, while seeking good ends.
Every error and oversight of The Enemy will provide new 'cracks' into which these good acts may be inserted. And all the time God is working behind the scenes to 'make the best' of whatever Good Men may do, and whatever 'oversights' evil may commit; in ways that not even The Wise can understand or predict.
This is a situation in which the impossibility of specific plans becomes an advantage; because plans cannot for long be kept secret, and will be defeated by superior power.
But the acts of Men who have taken the side of God and whose courage is sustained by hope of eternal resurrected life; cannot finally be defeated but will always lead eventually to good outcomes - when they are being insensibly organized by the higher wisdom of divine providence.
And the 'small oversights' intrinsic to evil will always be providing new possibilities and pathways by which such good may be done.