There is a leniency and stringency each way depending on the context:
Shulchan Aruch mentions the muktza status of bones separated from their meat twice: in Seif 27 and Seif 29. In Seif 27, Shulchan Aruch states that although the bones are no longer fit for human consumption they are not considered muktza as they can still be given to dogs. Seif 29 rules that animal food is only not considered muktzah if the animal that would eat it is common to that area. Based on this, the Rama there justifies the ruling in Seif 27 that meatless bones are not muktza, as dogs are commonly found animals.
In Seif 27, the reason we might have considered such bones muktza is because they are similar to nolad; we now have animal food that was "made" on Shabbos when the meat was separated and they became no longer fit for humans. Since Shulchan Aruch rules that they are not considered muktza, it is a kal ve'chomer that if they were separated before Shabbos they are not muktza as there is certainly no question of nolad.
Seif 29 defines the parameters where animal food is considered muktza or not. According to the Ran (the way the Rama understands him in Darkey Moshe; see Biur Halacha 29), even if animals are commonly found in the area, one who is not a pet owner cannot move animal food on Shabbos, since for him it was not prepared before Shabbos. However, the Rama rules like those who argue with the Ran, and hold that as long as there are animals commonly found even a non pet owner may move animal food. The Ran himself though would agree that if such animal food only became suitable for animals on Shabbos, but on Erev Shabbos was fit for humans, then even a non animal owner may move it as it was prepared for him before Shabbos. Thus in this case the novelty is the other way round; if the Rama rules against the Ran that even if the bones were separated from the meat on Erev Shabbos they are not muktza, certainly this would be the case if they were separated on Shabbos where even the Ran would agree.