Very good points.
Of course the background incentive is the desire to offer something of hope without being disingenuous. The problem arises when you personally can’t see any hope for them yourself. At such times, being blatantly honest is generally a really bad idea. Thus the phrase, “let me know if there is something I can do” is very good… assuming it was genuine.
I personally do any of 5 things in such cases;
1) offer the best sign of hope that I can think of at the time; perhaps, “this too shall pass” or something similar.
2) “Let me think about that” and truly contemplate if there really is something that I can trigger such as to help (often finding money to give to them) and holding to a degree of integrity.
3) don’t except the notion that if I can’t think of it, no one else could either. And thus I refer the problem to someone else who might know something. Thus, "let me see if I can find someone to help with that".
4) On very rare occasion I will say, “I’ll pray for you”, but that is only because I know how to do it to get results. The problem is that at times, what is happening is actually the better thing for the person than they realize or could fathom. Thus my prayer effort might well lead to “Don’t touch the issue. Let it ride”. So I tend to hold off such a phrase until I can be more assured that I actually will get real-world positive results. And also, I tend to just go do it rather than say that I am going to. That way, I don’t get into silly arguments as to whether there really is a God with someone who really isn’t in a position to be bitching, religious or not.
5) I might even give a little explanation; “A “miracle” is merely a positive occurrence that no one thought could happen. We aren’t bright enough to rationally dismiss miracles. I know. I have arranged too many myself, even to my own surprise. So don’t fall into that silly trap of contemplating the negative (worrying) to the point that you presume it and perhaps even cause it. Since you think that you can’t fix your situation, perhaps it is time to let go and let someone else take the reigns for at least a short while.”