
The arrows in the image at the top of this page point to the feed dogs on a sewing machine. These are the “teeth” that grab the fabric and move it along when you press your foot against the pedal that makes your sewing machine move.
Those of us who have been sewing doll clothes for a while have run across the problem of not having the feed dogs “catch” the material, whenever you’re sewing a tiny strap or belt for a doll. You can see in the image below that the feed dogs don’t actually touch the material of my doll’s shirt strap:

So how do you get the fabric to move along?
Well, it’s not recommended because you can break a needle this way, but I actually grab the tail of my thread at the back of the presser foot, and gently pull my garment strap along.
This doesn’t keep your Barbie belts or garment straps from dipping down into the hole for the bobbin though. Don’t you just hate when that happens?! Ugh! So do I!
And I can tell you it’s not a fool-proof prevention, but one piece of advice I can give you is to start your stitches a quarter inch (or 6 mm) from the raw edge of the strap’s fabric. Also, end your stitches one quarter inch from the edge of the strap’s fabric too. Don’t go all the way to the very edge.

Another suggestions I have is this: only move your straps and belts forward in the sewing machine. Don’t use the reverse feature to tie a stitch-back-and-forth “knot” at the end of your stitch because to do so, is definitely asking for trouble!
Instead, just give your straps and belts a single-direction stitch without ever backing up.
Now, if you’re worried that your threads will unravel, make the tail at the front and back of the strap or belt really long, and tie the two threads in a knot at each end, just like you would with shoe laces:

But my final piece of advice is the one I actually follow, myself, for the most part. Just whipstitch those tiny belts and straps by hand! It will save you a lot of heartache!

I really only use a sewing machine for belts and straps if I’m in a rush. The rest of the time, I sew them by hand, and I always feel like it has been time well-spent because my sewing machine didn’t eat my strap and wind up with a bad case of indigestion.
All good suggestions. I would add that the use of a ziipper foot for narrow pieces may help.
Awesome! Thank you for adding that helpful tip, Cyntia. 🙂