The fix is straightforward: require evidence of the debt upfront, and if you're attempting to collect on debt you can't verify was agreed to by the person you're pursuing, damages are substantial (say, $1M per occurance). Make reporting of violations via the CFPB frictionless.
You will see debt originators rapidly standing up robust identity proofing systems (having customers come into a branch with their IDs), and asking Congress to legislate their implementation (Login.gov and similar for private enterprise, with the end game being a usable national ID system such that Estonia has [1]).
Tangentially, current risk management in this space between identity and finance sucks. I worked with someone to get liens off their Lexis Nexis Risk Solutions report (which mortgage originators use for compliance purposes with conventional mortgage underwriting guidelines as it relates to foreclosures and real estate fraud) that were on their report for almost 8 years in error. It took a CFPB complaint for Lexis Nexis to remove them with citations from an attorney to state statute, and this data isn't classified as consumer reporting, so it's almost impossible to obtain financial recourse/damages for these occurrences.
[1] https://privacyinternational.org/case-study/4737/id-systems-...
[1] https://news.ycombinator.com/item?id=29980189 (HN thread of the above link)