It also needs to be taken into consideration that if this person is living close in any sense of the word, in that going without even a few weeks pay might really upset the applecart of her life, then quitting and filing a claim for unemployment is not a very good option. It is not nearly so simple and cut and dried as "you need to quit and can collect unemployment." Even if the person is going to be approved, which is by no means guaranteed in these circumstances, it will only be after, in the very best case scenario, six to eight weeks of wrangling back and forth without any money coming in whatsoever. When and if she is approved, yes, she would be backpaid for the weeks that she had certified for since filing, but unemployment is likely going to be less money a week than they were making working, even at the reduced hours and the reduced pay. And after a certain number of weeks, max six months, it will come to a screeching halt, regardless of whether the person has found a new job or not.
I'm much more a fan of looking for another job before you leave the one you've got, even though you have been punished by a reduction in hours and pay. And as it has been pointed out, once you have worked at the new job, with the understanding that you are receiving reduced hours and reduced pay, this is considered accepting the terms of employment offered by the employer. So if you then quit and file a claim for unemployment, your chances of being approved for benefits grows even smaller.