I went to post this on this Inkscape forums since that's what I'm working in, but since I'm a new member my post has to be approved my a moderator, which will take who knows how long, so I'll try you guys here.
I have no idea how to properly explain what it is I'm trying to do (if there's a proper name for it, please tell me!). So I'll try and explain it with a picture that someone else made that illustrates what I'm trying to do:
(I just noticed it's kind of hard to read the blue text. The top line says "And curls up 'into' the object" and the bottom line says "While also continuing the outline here")
In that picture, the outline of the paw curls up and "into" the object, while also continuing the outline of the paw. How is that kind of effect achieved in vector graphics?