Last time I read Ringworld (a couple of years ago), I was struck by these two passages (on page 234 of the paperback edition that I own (Del Rey 1981: 19th printing)): Nessus says "Land anywhere on the Ringworld and dig. What do you find?" "Dirt" said Louis "So?" "And then?" "More dirt. Bedrock. Ring floor material," said Louis. And as he said these words, the landscape seemed to alter.now the landscape showed as the shell it was. The difference between an honest planet and this was the difference between a human face and an empty rubber mask." Following this, Nessus talks about how Ringworld is a trap once civilization falls. Later, on page 322, Louis compares Teela to a hollow mask, using much the same words and images that he previously used in describing the Ring. When I recognized this repeated imagery, my picture of the novel changed quite a bit. Allow me to explain in detail.
When I studied Ringworld as part of Professor Frank Wilson's philosophy classes, we learned about three categories of novels: mimetic, which are plot-driven, featuring relatively few coincidences and generally driven by decisions by the main character and the consequences of those decisions, descriptive, which are intended to illustrate some object or process (like many of Michener's novels) and use enough coincidence to ensure a full picture is given, and didactic, which are intended to make a point, and thus have coincidences as necessary to get the point across (Note that didactic is not a pejorative - there are plenty of good didactic novels).
It's pretty clear that Ringworld is a didactic novel - though titled as a descriptive novel, the main characters don't actually get to the Ring until quite a bit of the novel has gone by, and of course, the characters only see a tiny fraction of the Ring; the plot is also not driven by the Louis's decisions as much as by the effects of Teela's luck (an author's tool for justifying coincidences). In my opinion, Ringworld is an exploration of the ideas of safety and risk, through four primary characters with very different approaches to those ideas, and a reductio ad absurdum argument against the idea of perfect safety.
As the passages I quoted above indicate, both Teela's luck and the Ringworld itself are idealizations of perfect safety, and both turn out to be masks that hide shallowness (literally and figuratively) that turns out to be a trap. Teela is perfectly safe under ordinary circumstances, even from emotional pain, due to her luck, and this has left her stunted psychologically, unable to empathize with the pain of others, in spite of her clear intelligence (several examples show how smart Teela is: she identifies the purpose of the Ring's radiator fins on page 114, she figures out how long the ship has been in stasis on page 122 (when Louis was unable to), she calculates the thickness of the Ring (assuming it has the density of hull material, which she also happens to know) in her head on page 80, etc.). Meanwhile, the Ring as originally designed seems ideal - three million Earth's worth of surface area for a population, with an environment throughout that is as pleasant as the best places on Earth, but it too is a trap, since if civilization collapses, the lack of easily accessible resources will make it very difficult for it to arise again (and in fact, without active control, erosion and other processes are one-way on the Ring, so ecological collapse will also occur once civilization occurs). Teela and the Ring are meant for each other indeed - Teela gets to experience dangers at least vicariously and learns to be fully human, while the Ring gets Teela (the potential ancestor of a civilization of lucky humans who will inhabit, refurbish and protect the Ring).
The theme of risk versus safety is further illuminated by Louis, Speaker and Nessus. Each has a different way of balancing risk and safety, whether they admit it or not, and Louis's middle-way proves to be safer than Nessus's (and his whole species') hubristic attempts to acquire safety through control of all possible dangers, and Speaker's pursuit of safety through intimidation of every possible threat. Furthermore, Prill's people provide another example of the ironic dangers of maximizing local, near-term safety. The collapsed Ringworld civilization could have rebuilt if Prill's people had been willing to risk their of stored power (Nessus lays out a sequence of operations that could have restored civilization on pages 290-291 in chapter 21) to make the effort, but - instead they pursued short-term safety dooming them and their descendants to a cascading decline.