Would you apply to jobs that pay less if you already have a job?

[Nikia]

Let's say that you have a job that you don't really like at a company where you have no future aside from what you are doing. You have applied to many jobs listing a pay range including your current pay rate or more. The jobs that pay more are supervisery type jobs and unfortunately your anxiety disorders become evident during the interview since a job interview is one of the most stressful situations for you and they don't want to hire anxious supervisers. When you go to the job interviews that include your current pay rate, it becomes clear that they don't want to pay you that much because they ask and the whole tone of the interview changes.
You make under $30,000 per year. You have a BA in biology and 5 years experience in food quality assurance. Do you swallow your pride and apply for jobs that pay less and tell the people at the interviews that you are willing to work at the lower end of their advertised salary rate?
Let's say also that you are in debt due to medical bills although you suspect that your current job might be causing some of the problems.
Let's say that the potential companies that you want to apply to are bigger and you are more likely to have a future there as far as promotions go.
I don't know if I can stand working where I do much longer. Sometimes, I wish that the company would close so I would be forced to get a different job.