How do I go about finding a place for my mom on short notice? AFC has notified me IF owner gets sick, I have 24 hours to remove my mom!

I would contact the licensing agency. Seems that there has to be a plan in place for all facilities. Call the Area Agency on Aging too.

Mom would be required to quarantine too. Seems like mom would be required by law to stay right where she is.

It sounds like a small board & care type of home if so it likely has as a requirement that the owner -who is licensing holder - lives on site or lives adjacent. If that is the case, should they / the owner not be able to be on-site, the operating license gets suspended. If it’s technically “Assisted” type of foster care, the residents are - in theory - capable to do their ADLs on their own perhaps with some limited assistance, so they can get notice to move in short order without mandated safe lateral transfers like a NH / skilled nursing care facility would be required to do. I know finding this out now doesn’t help your situation, but It can help explain why it can happen.
Under more normal times, the residents would likely go to the ER for a break or fall or if place was closing get a needs assessment done by the division of state govt licenses foster care homes. I’d suggest you try to find out what office deals with foster care program or board & care homes ASAP to see what possible help they can be. If its off to ER that ends up happening, family or the discharge planner at the hospital deals with finding new placement. But right now the hospitals are doing whatever they can not to take anyone in and discharging patients ASAP or putting off all nonessential surgery as there is the tsunami of Covid-19 anticipated. Hospitals seem to be planning that US is going to follow the case trajectory of either Italy or Spain and so hospitals will be overwhelmed, just not enough beds

If family doesn’t or cannot come and get an elder from the ER or from a facility that has given notice to vacate, what usually happens is that they become an emergency ward of the state with an interim guardian appointed. The Area Agency on Aging that Glad mentioned should have info on all this. If not, usually this is done in probate court (judges usually have list of vetted guardians at the ready). If AoA not helpful, you might go online to see how emergency guardianships are done & then call the court Monday. The courthouse staff are usually super helpful and good in panic situations.
There's going to be others in this same situation. If moms city actually has local TV station, I’d e-mail one of the reporters ASAP about all this to see if they can do a story next week. Be sure to send couple of fotos of mom attached to the email too.

if mom has the ability to private pay, and her care needs are pretty routine, there will be another facility that will take her. If she’s Medicaid, and you cannot take her in or private pay for her, personally I’d let her become a ward of the state with an appointed guardian as that guardian has lots of legal authority and can get things done you couldn’t do easily even in the best of times. Could be that there’s 3 ladies there all in this situation. Try to reach out to other families to see what they are doing & perhaps all 3 move to the same place in a more remote area of the state. Good luck.

Gut reaction is if she becomes sick I would think that quarantine measures are in effect and she could not be moved until she is well.
I would contact whatever agency licenses the facility and ask what the procedures are in this case. I think at this time what is "normally" done is out the window as there are no places for people to go. You do not want to be in the hospital, most facilities that would normally accept someone are on lock down.

Have you any paperwork , from when you placed her in the home? Check the paperwork and see if you have any recourse. Good luck.

If your mother and the other residents are exposed to Covid-19 thru the caregiver, then it will be difficult to find a facility who would take them. My 95 year old FIL is in a facility now as is my 89 year old mother in a different place; both on lock down. I doubt or at least I hope they would not accept a patient who would have been exposed, even if a test was negative. All of the families with members in this home need to determine plan B with the caregiver and also the local health dept to determine what actually could be done if this transpires, which it could.