How do you do an intrude instead of extrude? Lets say I want to decrease the height of the back of the chair, or all of its legs, how is the easier way to do it? I mean without cutting each of them into two pieces and deleting the remaining parts.
If I choose all the bottom faces of the legs, press E , and then drag up, it will create hollow spaces. Same thing probably applied for the back of the chair.
The answer is to simply just grab all the faces on the bottom of the chair, press G to grab them, and press Z afterwards to pull the faces only vertically. This isn't intruding, but just moving faces. Simply put, drag the faces up without pressing E, in the case of the chair legs. I hope this answers your question!
On another note...
if you press I, then inset faces, and then extrude, moving up into the mesh, it will create a hollow space with depth, rather than just 4 faces with no cap. This second response probably doesn't answer your question, but this is probably what 'Intrude' means in Blender.