I was once a developer at the end of a chain like you describe. My client had been subcontracted by a company that wasn't telling the big client they were working for they were subcontracting the work, and my client didn't tell them they were subcontracting to me.
Here's what happened: I had been told the whole thing had to be finished in six weeks. The money was ok for six weeks, but not outstanding. I took it anyway, because it just happened to be something I really was looking to do at the time.
My client's client never once met one of their deliverable deadlines. So, when it came to date I had originally expected to be paid, we were only halfway through with the project. I did get paid though, as I wouldn't upload something that they really wanted to show the end client.
When I was finished with my part of the project, I asked them to verify that it worked to the end client's satisfaction, and I went and got a full-time contracting job elsewhere. To this day, I have no idea if they made any effort to get the interim client or the end client to test anything.
A couple of months after that, they came back and told me that they had found some bugs. I frankly didn't have the time to sell, and I sent an email reiterating that I'd asked them to make sure the client was happy before I walked away. Believe it or not, they forwarded that email to the the interim client, essentially passing the blame on to them (where I'd only said that I'd made the request of my client). By the end of this, none of us looked very good.
All of this is a long-winded way of saying that if you don't tell the client that you're subcontracting
- You can't tell them that your contractor needs to be paid by the 1st, whether they provided the deliverables she needs to finish the work she was supposed to have done by the 15th or not. But you better be prepared to cough up that money, since she has to eat and probably turned down other work to take the work for you.
- If something goes wrong and the project stretches beyond the planned time, you need to be able to go to the client and get them to provide an incentive for the contractor to stick around. You don't have the flexibility to ask someone else to put their life on hold for a stop-start project the way you personally can, and they have every right to wander off and get other work while you're not directly paying them.
- If the contractor completely screws the pooch, you may not be able to 100% avoid taking a financial hit or a hit to your reputation, but most clients are going to be a little more forgiving of "you were unwise in hiring a contractor" than "you just do crap work."