Yes, the best way is to use a "mouse" (leader fabric). Sew onto it in the beginning and off on another mouse at the end which then is ready on the machine for the next sean. If you chain you are automatically doing that and only use very few of the "mice".

I have the janome 6600 and the janome 6250 and they both do it. The only one I haven't had this problem with, is my featherweight.

This helps...get into the habit of grabbing the thread ends at the start of the seam. Hold them firmly and out straight as you start to sew. Once you have a couple of stitches done you can let go. It helps with the needle eating the fabric and with losing the needle thread due too short a tail. Once you have the habit, it is so automatic you don't even think about it anymore.

I use the leaders and enders, but also make sure your seam is in far enough for the feed dogs to have something to pull.

Hold on to your top thread when you start sewing, and hold it for about 3 stitches.

My featherweight and treadles don't eat my fabric. I prefer
a straight stitch machine when I'm piecing with triangles.

Hi ~ My Diamond Husqvarna does not do that, but I believe that yours won't either with the following trick. Turn the needle rotation until the bobbin thread is pulled up to the top plate. Use tweezers if nesseccary to grab the bobbin thread. When you start to sew, hold on to the bobbin thread along with the top thread and you will not have a problem ;)

One instructor at my LQS calls this a "thread catcher" - its a scrap that is folded to double thickness. Always begin sewing on this piece and end on it. This gives your machine a chance to feed well, and you can also check tension, stitch length, thread color, etc. It also prevents you from having all of those tiny bits of trimmed threads all over the place! I love it!

And make sure you are holding the upper and lower threads coming up from the bobbin and also off the needle. If you don't, the feed dogs will grab your fabric and you run the risk of the nasty thread nests.

And if you make those leaders and enders some squares from your stash, you will have the start of another quilt painlessly.