Most of the time, they will get something back that is awful, and if they actually have an eye for quality, it'll make them better appreciate the work you do. You might even get some more work from them after they've satisfied their fantasies of cheap labor.
If they don't have an eye for quality, and they go with the garbage the outsource comes up with, then you probably didn't want them as a client in the first place.
They go off and spend $7,000, then come to me because it wasn't done properly and say, "Unfortunately, it really didn't work out with these other guys - can you please, please help me out?" Now the problem is that they only have $8,000. Where before I might have been able to cut scope a bit to get down to $15,000; or perhaps they could have scrounged up another $3,000, they are now completely out of luck. And it sucks to see this happen to people.
On the other hand, sometimes people who charge less do a great job. As much as I'm not the cheapest person around, I'm also not nearly the most expensive, and I still do good work. To someone at the high-end, perhaps I'm one of those low-cost, risky alternatives, although I don't see it that way. The problem for the average client, though, is they generally lack the experience and understanding they need to properly evaluate all of their options.
In these situations, I usually offer a normal bit of criticism, both positive and negative, and then let that be the end of it. Sometimes the client will come back, sometimes not.
Either way, you've preserved your relationship and they might well come back to you when they want to see some revisions down the road.