Extreme Libertarians refuse to engage in a sensible discussion on how to solve this in practice, instead contenting themselves with repeating mantra's such as "the market will sort it out" or "property rights".
Arguably, if the entire universe is a market, the "market" does sort everything out, in that everything that exists, exists because the universe allows it to exist.
This of course makes "the market will provide X" indistinguishable from a null statement. Of course the market will provide X; the market is everything that's possible. But at what price will it choose to provide X? "Zero quantity of X for infinity dollars after infinite years" is a perfectly valid solution of the supply/demand equation. And "the market will provide War, Terror, Starvation and Death for 1000 years for 99% of the population, and Bohemian Luxury for a tiny elite" is also a perfectly valid solution.
To subvert a common libertarian example - if someone points a gun at me and says "dig your own grave or die right now", they're not actually taking me out of the market mechanism to do that. They're simply providing a rational choice (dig or die), a service (not immediately shooting me), and a charge (my digging). It's a valid contract, and I have the choice to accept or reject. Obviously if I reject the contract I may die, but - Atlas shrugs - that's life, isn't it? The market as a whole sees no self-interest in my continuing to live unless I provide it with services, and if we get really technical and precise about decoupling every private action from empathy, just *because* someone pulls the trigger on the gun they privately own and control, doesn't mean I'm *necessarily* going to die - I do also have the choice to dodge out of the way, etc, etc. There really is no there there in libertarianism; we can keep playing the "I'm not responsible for your happiness, even though I can logically foresee that the result of my actions will hurt you" game forever.
The problem is that as humans we have actual concrete needs which we would like actual concrete solutions for inside a feasible timeframe, and not just an abstract "well, you'll get that if/when it's possible for whatever price you're willing to pay". And sometimes those solutions require more than just shrugging and assuming someone else will solve them, which is what free market theory boils down to in the end.