I have been caring for my demented Dad for 8 years, what would happen if I took him to the ER and did not go pick him up?

What do you Want to Happen

The short answer is they will treat him for what you brought him there for, and release him.
This brings many more questions than answers.
Can he effectively communicate with people treating him?
Do you have POA? Legal health papers?
If he has no place to go they will order assisted living or. nursing home for him.
Someone has to sign the release papers. Also the papers to go to assisted Living.
Has he insurance? If not we go to Medicaid.
Host of other issues that will need to be considered.
You need an elder law attorney to set up legal papers and help you understand what your position and his are, or will be.
There is no simple answer that can answer this question.

I would hope for some permanent help. Such as placement in assisted living or nursing home. I am finding it difficult to find any meaningful assistance. For example, the county offers day care. This situation is well beyond daycare.I know that elderly without children get assistance but it seems that if there is a caregiver avaliable help is hard to get.

Zander, many people do this as a last resort. If you are the POA, you could be charged with abandonment, so immediately resign your POA in writing. As long as you haven't been taking money or co-mingling bank accounts, there is not much they can do to you. You should let the parent's MD know how desperate this situation is. You should let APS know how bad this is. You should let family know you can't do this anymore. Of course, if you are living in his house, you are out of there immediately.