Walking in real life has been called controlled falling by some analysts. We don’t consciously think about weight distribution and balance while we walk but these issues become glaringly evident in stop motion and gravity becomes a primary nemesis.
So how do you keep the puppet from falling down? There are many inventive methods people have used over time. Some involved using electro magnetic plates under the table that are turned on and off to hold characters with metal feet. I suppose an assistant applied the plate and turned on the current while the animator held the puppet in place. I’ve tried a variation using just strong magnets and found the snapping of the attracting materials together would kick the puppet out of place and I gave that idea up pretty fast.
The most used method is the Tie Down where the puppet armature has a split channel in the toe area. The puppet usually has a shoe whose toe area comes off or flips back to reveal this channel. Animators will mark a spot on the stage floor in the puppets ‘toe channel’ of the supporting foot. The spot is drilled and a screw is screwed in half way. Then the puppet is slid into place using the toe channel around the screw which is then tighten down to hold the puppet upright. Animation of the walk goes on with all the support on that one tied down foot until the other foot is ready to plant and then the process repeated.
There have been variations where the floor is predrilled with holes and the foot tied down from below thru those holes but it’s essentially the same.
Now with digital rig removable it’s become more common to use a flexible arm that supports the character and can be clipped onto set pieces and moved around to accommodate the action. The character can walk, run, jump or even hang in the air now so gravity can just take a hike for all I care.