I'd assume that, as long as they're careful about how they pressure you, it's not fraud if you decide to pay. AFAIK they're under no obligation to volunteer that you don't have to pay them anything, or to otherwise educate you about the fact that they're (in fact) just begging for money they're not owed, and hoping you'll give it to them. But if they ask you (the aggrieved, in the middle of hosting family and trying to plan a funeral and figuring out how to pay all the bills you actually do need to, as a result of all this) to accept this debt and you say you do, and then they help you work out a very convenient and gracious payment plan for this debt you unthinkingly accepted because you're not a damn lawyer and you're kinda stressed out and debt collectors are scary and now it's on auto-draft for the next 18 months, well, that's above-board.

I've known people who've been on the receiving end of those calls, so they definitely happen, and must be profitable, one way or another.

If it isn't fraud, it should be. The lack of liability or any requirements for due diligence for debt collectors is a utter travesty that primarily harms the most vulnerable and underrepresented people in our society.