I really don’t know what to do with this problem.
Here you can see a human model that has goggles. These pair of goggles are not connected to the head of the model itself. What I mean here is that there is no edge / face connecting the vertices of the head and the goggles.
When I try to change it’s pose, all the parts that are not connected to the main body are left behind.
Is there any way I can fix this without connecting all the parts together?
Either parent them to the bone, or use a constraint like “child of”. The latter is helpful if you need a piece to stop moving with the head at some point in the animation., like the character taking their googles off.
You just need to fix the weight painting of those detached mesh pieces. Automatic Weighting can’t catch everything and it does particularly badly with separated meshes. Keep the armature in Pose Mode and put the model in Weight Paint mode. Select the bone you want to control the goggles and paint some influence on to them until they behave correctly.
Weight painting did the trick! thanks K Horseman 
I was having the same problem, and I finally figured it out!
First, in object mode, select the parts that aren’t sticking. In the Modifier Properties, under Armature, make sure Bind To > Bone Envelopes is also selected.
Then select the armature. Switch to edit mode, then select the head bone. Under “Bone Properties,” increase the envelope distance until the face parts start sticking to the head.
This drove me crazy, and weight painting wasn’t working for me. Anyway, hopefully, this will help somebody! Peace.
