So instead of phasing out transfer payments at the low end, you reduce bureaucracy by introducing a universal payment, and balance it out at the high end with progressive taxes.
Someone who chooses to work and earns an additional $20,000 per year would still see a real benefit from their universal payment.
Someone who chooses to work and earns an additional $200,000 per year would be taxed such that their universal payment is essentially zero.
In either case, I don't see anything special about these jobs that would make them the first to disappear in the face of UBI.
A possible example would be many cast food positions. If the workers didn't have to work together by wages would go up driving up the cost of fast-food. The higher cost would lower demand, and it might not make sense to have 10 fast food restaurants on every block.
But now we're back to one of the key criticisms of UBI - reduced labor supply leads to higher wages but reduced employment, increased prices, reduced economic activity and consequently decreased consumer surplus (which would be a bad thing).