Hi Sara,
First, I must say that I have never kept millipedes so I cannot answer this specifically. If you can upload a pic of the "remains" it might be helpful.
What I can tell you is of my experience with rearing large caterpillars, which also molt 5 times during this stage. A couple years ago I had a luna cat that had difficulty during a molt and some of the skin was stuck around its body about .25" from back end. It seemed OK but did not eat as much. Like you, I watched carefully during its next molt. Because the cat had continued to grow, but the remaining skin had not, it began to “girdle” it. I tried to soften the skin and carefully remove or at least cut it. Believe me - it was very delicate and scary "surgery"!! Unfortunately, it died not because of the constraint so much as that it was unable to poop. What went in could not come out
I put it in the fridge then freezer to quicken its demise and upon “dissection I found its entire inside just full of frass (caterpillar poop).
So, I tell you this b/c it may have been what happened to your millipede. The “mucous” may be the remains of undigested food. Again, this is sheer speculation on my part and maybe someone who keeps these and has had a similar experience can add something to this.
You sound like a caring “mom” and I am sorry for any sadness this experience has brought to you 
lele
>>Hi, I currently own 20 black african millipedes that were born Nov 2003. They are growing up very nicely and are now getting their dark black color. My question is over a concern I have for one of them. About 2 to 3 months ago, this particular millipede, molt like it was suppose to, but a small section of his middle did not come out right and so his middle was smaller then the front and back side of his body. He also could not use his legs in that section. Well starting last week he started to molch again, so Ive been keeping an eye on him. He has been doing very well til this morning. This is what I found where he was molching:
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>>His molch remains were thick, with a small hole in the middle.
>>The molch was almost straight and not curved.
>>There was a yellow thick mucas inside on the bottom half of the molch.
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>>But no millipede.
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>>I could not find him, so Im wondering if he would actually grow smaller, basically redoing his end piece where the injured middle was, what the thick mucas is, if he really did heal himself, or have i lost him .
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most of my millipedes have started enjoying being on the top of the soil so I have most of them wondering around so if his middle has grown back it is hard to find him)
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>>Thank you so much,
>>Sara Dale