Negotiating power is derived exclusively from the ability to walk away. When walking away from your employment means being evicted, starving, and being unable to afford medical care, your ability to do so is crippled.
A UBI should cover the cost of housing and food, though it does not guarantee that you can live in a highly-sought after area without other income. That must be factored into employee compensation in the same way that it already is for desirable jobs today. It puts more pressure on cities to ensure that close, affordable housing exists for the lower-wage workers like retail and service workers who help make those cities desirable places to live. A job at a swanky downtown coffee shop with an hour commute becomes a lot less attractive if I can ditch that job and the transit costs without worrying about my basic survival. So the coffee shop has to increase pay or lose its employees and close up. Its downtown location and clientele will either absorb the price increase, or downtown will become a less competitive living space due to the loss of the business.
A UBI will not remove all of the reasons someone can’t pack up and leave if the area is too expensive, there are lots of human factors in play, but it will increase people’s ability to move elsewhere without having to fear for their very survival.
medical bills is supposed to be solved by universal health care.
housing is another issue that can be solved one way by relaxing zoning ordinances for the purpose of increasing the development of affordable housing.
This can be extended to other social services such as childcare.
The vast majority of people who receive unemployment had an unplanned job loss, which already puts them at a disadvantage both planning-wise and psychologically. If instead you KNOW that you will receive income when choosing to leave a job, you are more able to prepare for how it will affect your lifestyle.