I quit my job to care for my sick mom. Do I qualify for unemployment compensation?

Unemployment typically requires you be available for and seeking employme

It figures........the son / daughter 'caregiver'.....gets screwed-over again......be good boys and girls......take care of your parents.....regardless.......go to any lengths to 'honor thy father and mother'.......and drive yourself nuts in the process......let your health suffer and quit your job and go broke and land in the poorhouse......yes.......being a 'caregiver' is just great!

To qualify for unemployment your employer has to fire you or lay you off. If you quit, unemployment is not available. Is there any way you can get your job back and work things out another way?

Unemployment is for people who are temporarily, and not of their choosing, out of work.
You make the argument that society should support you for taking care of your parents, you can also stretch that argument to say government should take care of low income parents or households.....and it does, through welfare and other programs. These programs are the poverty safety net, regardless of what leads someone to the need. (Caregivers, single parents, etc.)
So, if your income qualifies, you may be eligible for welfare. You parent may be viewed as a dependent. If you live with them their assets and income may be considered as well. If you need financial help, you may want to look into welfare instead of unemployment.

Unfortunately welfare is typically much lower income than a job, but it is something. So, working and paying for day care may be more financially sound, but it may not be the best decision.

Best of luck,
L