What kind of mattress pad prevents bed sores?

Sounds like you have two issues: Getting in and out of bed safely; and avoiding bedsores. Addressing safety - has mobility been discussed with her doctor? Maybe equipment can be prescribed? As for the mattress, there are manufacturers that make mattresses to help with that problem. When hospice recommended one for my Dad, the manufacture read, "Sentech".

I know equipment can be expensive. In my area there is a group called Bridge Ministries that folks can go to for all sorts of needs. They ask for donations in return but if folks can't pay, they aren't turned away. One of the greatest groups I've seen in operation. Maybe there is an organization like that where you are.

If she's still mobile I don't think you need to worry too much about pressure sores yet. There are Geo-Matt mattress pads which are designed for this, but that won't stop her from sinking into the memory foam... it does make it difficult to get up and reposition, doesn't it!
I would look at getting a hospital type adjustable bed, the idea of putting the bed on the floor doesn't sound like a good one to me if she had trouble standing. If she is resistant to that at the very least add in a hand rail/grab bar that slides under the mattress and gives some assistance in standing.

MilshyHaran, at the rehab facility where my Mom is currently living, they use some type of air mattress. And the bed itself is lower to the ground compared to a typical home bed.