I've always used kolinsky brushes for both painting and nails. They're both constructed and assembled the same way. Cheap brushes do have shorter hairs, and are held together in the ferrule with bad adhesive. And because they're most likely mass manufactured, and not hand assembled like a higher quality brush, there's not enough tension in the ferrule due to incorrect size, and with the hairs falling off, even more tension is lost.
I've been given quite a number of cheap brushes through the years as gifts. Pinching it gives it tension. I keep my cheap and newly restored brushes for doing things I would never do with a newer brush. All of them (both cheap nail and painting brushes) are now used for mixing paint on pallets, applying loose bits like glitter, splattering or rough blending paint onto canvas, spreading glue onto hard surfaces to apply charms and crystals, ect.
Sorry for my earlier comment. I shouldn't have left anyone with the impression that they should train with a cheap brush. Cheap brushes are only good for using on tasks you'd never use a good brush for. If you're not a painter or crafter, it's pretty much useless to keep one around. You should invest in a good quality brush as suggested by many.