If it is self-defeating, it is not more efficient. And we already have a bureaucracy whose functions include verifying income claims and adjusting net payments based on them in the income tax system, we don’t need a bunch of different bureaucracies doing that redundantly with slightly varied definitions and rules and paperwork that serve little practical purpose besides justifying additional bureaucracies and enforcing self-defeating funding cliffs.
It is possible that there would be fraud around pretending to be a person when that person doesn’t exist, or continuing to collect benefits for someone who is dead.
But “are you a live person” is much harder to fake than “did you make sure you didn’t do these 6 illegible things that would make you ineligible”.
When you eliminate means-testing in favor of income taxes and eliminste the myriad different definitions of income and assets for qualification for different programs and the opportunity it creates (and the incentive funding cliffs create) for specialized benefit fraud, there is no special “UBI abuse” to monitor for. You have to monitor for tax fraud, but we’ve got a bureaucracy doing that at society-wide scale anyway.
If it was gradual withdrawal rather than a cliff, she could afford to take the job.
The UK's Universal Credit is supposed to be gradual and therefore work out to everyone's benefit. But in practice it has few of the good qualities of either UBI or negative taxation. Universal Credit has plenty of nasty cliffs, complicated rules and cruel penalties that push unlucky people deeply into poverty, and it also has an extremely heavy administration cost - every employer must file everyone's individual employment taxes every few weeks online and face heavy fines for getting anything wrong or being a day late.