How can i create a seamless blend between two objects and give the illusion of rubber stretching? I'm trying to recreate this seamless, stretchy illusion between the character and environment as seen here: 



but have no idea how to do it? I've tried extruding particular faces of the floor plain but when it comes to curving it, the "stretchy cord" just doesn't look right, can anyone help me?

(images by Jun Seo Hahm)
Add a plane with some subdivisions: hit W then S (in 2.79) a few times. Add a cube above it, adjust its scale then subdivide it a few times. Delete the faces at the legs in the cube and in the plane (one face/leg). Select the edges around the holes both on the cube and the floor, then bridge them with "Bridge edge loops" command. Then add a "Subdivision surface" modifier to the mesh. You can correct the legs with new edge loops by hitting ctrl+p.