My farm animals I made on the 1st birthday cake stood up on their own after they were dried. They stood up fine. If the legs or whatever is to support the figure is very thin compared to the upper portion being supported you may need to put some sort of dowel or tooth pick in to support the extra weight.
Lots of times I've used lollipop sticks to support the figures--either by attaching them to the back of the figure, or building the figure around the lollipop stick (for instance, for a person, I may actually put the head on the top of the lollipop stick and work my way down.
On the cakes I have done that the figures sit directly on the buttercream, I have put pieces of spagetti in legs, coming out the bottom of the feet. That way the spagetti goes down into the cake to help give a little extra support. I also have done figures that I have attached to a cake board covered in fondant. For those I just attach using a little bit of water and when it dries, it actually becomes pretty sturdy. On my husband's car cake, I attached him to the board with water. On my Children's day cake, I had the spagetti in the legs to help hold Noah upright. Hope this helps a little.
A great way to make the figurines is to stick a skewer/dowel through a piece of styrofoam, and then build up the figurine. It will support it, and when your done you can use the skewer as extra support by driving it thru the cake. Another good thing is to mix in some tylose powder or gum tragacanth into the fondant to help it dry out faster and not become droopy. I always prefer to use gumpaste for figurines for this reason.
HTH
what size are you thinking about? I had a little girl jumping on a trampoline and she was about 6 inches high and I put toothpicks in her feet, I'll see if I can attach a picture of her. But she stayed up with no problem. I also put royal icing on the bottom of the feet.
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