Jeremy,
As you know, real property records in the US are maintained in a recording system. This is different than a registration system (think what we have for cars). You can record anything you want at the recorders, and the recorders only real responsibility is to make sure its signed and filed in the proper place. This is unlike a registration system where the framework dictates what you can and cant do. Try transferring your car title at the DMV while there is still a lien on it for example. The benefits of a recording system include less expensive administration and freedom to contract (also property doesn't lend its self well to registration because its hard to define, changes over time, and doesn't go away. Cars have simple vin numbers.)
Title insurance companies basically sprang up as a market response to our use of a recording system. Since the administrator (recorder) isn't setting any rules people wanted insurance to guarantee that they were buying what they thought they were being sold and lender were secured where they thought they should be: enter title insurance. A title company is not an agent of the recorder and has no interest in the terms of what is recorded. They only care that the docs were signed by the proper parties and sent at the right time to the proper place so they wont be liable for an insurance claim. The responsibility of enforcing a lien is squarely on the shoulders of a lender.
So, say you deliver your executed purchase contract to your favorite title company for closing. In the contract you write that the you will take title 'subject to all liens and encumbrances.' The title company pulls their title commitment and listed on schedule B exceptions will be the 1st position hard money lender from your example. What this is saying is, 'we the title company will give you insurance for everything we normally would (seller has marketable title and can sell to you, the taxes are paid, there aren't any strange easements etc.), but we've notified you that this lien is there and we wont pay you any insurance if they try to collect or make some claim on title.'
So you review the correspond lien docs the title company provided for you as part of their commitment and get a feel for that lender's terms and conditions. Based on what you find, you and the seller make a business decision on if you want to move forward: how big an institution is the lender, will you keep paying the loan, is there a due on sale clause, what is the risk the seller will find out someone different is making the payments, how quickly can you refi or flip it etc etc. I will say briefly that you can mitigate a lot of these risks by using creative structures, but Ill save the details for another time.
So in summary, the title company's job is not to pay off all liens. It is to do what ever you tell it to in the sales contract or escrow instructions. If you accept certain exceptions they will happily give you a limited warranty deed. Its the banks job to enforce the terms of their arrangement, not anyone else's.
