Whilst it seems at face value that the nursery is pushing their luck, I think it very much depends on the wording of the contract she has signed with the nursery - which of course is legally binding.
My daughter works in a nursery, and she has been furloughed although the nursery was going to continue to open for children of key workers.
However, they gave their parents the option of giving them one month's notice or paying 50% fees to retain the place for when thing return to normal.
However, my daughter has received an email yesterday saying they are considering the possibility of making redundancies, so who knows what's going on there.