She's mentally ill but does not see doctors or have medication. She receives no income, has no health insurance and has been taken care of by a previous partner who has been deceased for few years and more recently been living off of my grandmother's income which isn't enough to really support the both of them. My mother was recently diagnosed with cancer and had to have surgery regarding kidney failure. It's clear that she shouldn't be left alone anymore but I have no clue about where to start or what to do to help her. She needs housing, income, health care.
Why isn't she getting disability income?
Likely you will have to start the process. Take her to a doctor, get her evaluated. Take her to social services and start the process. Unfortunately, 55 is late to be thinking of these things.
But, be aware, depending on what state you and she reside in, that filial responsibility laws can apply.
To get the ball rolling, have her complete her advance directives and select her POAs for finance and health. If she has no income and insurance, I am sure she could qualify for Medicaid in her state of residence.
Is your father still alive?
Contact Hospice.
With the diagnosis of cancer and kidney failure she would qualify. (If she is not doing aggressive treatment)
You will have a Social Worker assigned to you and the Social Worker can help you navigate the process for Social Security, Medicare and Medicaid if needed.
(if you are in the USA I do not understand why she is not on Social Security and Medicare)
In any case Hospice will provide supplies and equipment that she will need.
Contact several and "interview" them. The Hospice that we use is a Not for Profit and the service and care is amazing.