Let's say you want to do a PhD in math. You love the subject, you'd like to make a career out of it, and you apply to grad schools. If a school wants you, though, not only will they admit you but they'll arrange some combination of teaching and/or stipend. If they admit you but want you to pay tuition, that means they don't really expect you to do well there. So a common rule for math and similar PhDs is that you shouldn't do one unless they're offering you full funding.

Or let's say you slip on the ice in a grocery store parking lot, and want to sue. This kind of personal injury case is typically arranged with a contingent fee, where your lawyer only gets money if you win. If, after talking to various lawyers, they're only willing to take the case as self-pay, that's telling you that they don't think your case is very likely to win, and you should probably drop it.

Other examples:

• After shopping your proposal around with an agent, do you get offered a book deal?
• Can you get venture capital to fund your startup?
• Can you get into a top-twelve philosophy PhD program?

You do need to keep in mind what is customary in different fields, though. If you're writing a kind of book where no one gets advances, then you can't take failure to get an advance as meaning much about you, though it does tell you things about the market for this kind of book. If you have an idea for a company that might need two employees and make $1M/year you won't get venture capital funding because they look for companies that will grow much larger than that, so failure to raise funds from them isn't a negative signal. [1]

(It's also possible for professional evaluators to get things wrong, and maybe you know something they don't. I would expect this most in situations where the evaluators' incentives and yours are not well aligned, where evaluators don't have the information to see how their decisions pan out, and where the market is too small for evaluators to have much practice.)

[1] Well, it would be a negative signal if you tried to raise money from them without realizing that this wasn't the sort of thing they're interested in funding. Though not a very strong signal, since "understands how VC works" is nearly entirely unrelated to what would make your small business successful or not.