Whether a stuffed animal can be machine-washed depends on the material it is made from. There are models that would not survive the spin cycle and the washing process in general. This detail is usually indicated on the label of the stuffed animal in question. Check the washing instructions on the label to confirm if it is suitable for the washing machine.
If the stuffed animal is broken or unstitched, it is not recommended to put it in the washing machine, as this could end up breaking it. Of course, if the toy has some type of electronic mechanism it generally cannot be submerged in water. To protect the teddy bear in the washing machine, one option is to put them inside a cloth bag.