Andrew R Stewart 

This forum has a "trial" period of posting before it will accept links and photos to be placed in a post. One way around this is to write out the address (spelling "at" and dot") of a third party photo sharing service, like Flicker (which is what I have used). The hope is that spammers and trolls won't have the patience to hang around that long and that real people will be patient, or go that small extra bit as I mentioned.

The OP said the chain drops off to the outside, between the small cog and the frame " It keeps on shifting until the chain jumps out from the teeth and get stuck between the teeth and the bike frame." This is the opposite of the usual result when the bike falls over and the rear der gets bent inward toward the spokes (and away from that between the frame and cogs point). It's quite possible that the pulley teeth are worn but this shouldn't make the chain jump off the cogs, maybe allow the chain to ride up somewhat off center of the pulley and thus rub against the cage plate. This is a different issue then what's asked about.

One very devious cause might be a broken axle. With power the freewheel, and rest of the wheel, can pull forward. The, now, two parts of the axle pull apart. The cogs become misaligned WRT the der (which is still attached to the frame, the other end of the broken axle). But this problem usually only shows with strong pedaling and not so much when the bike's rear wheel is lifted off the ground.

This is one more reason that more info is needed for us to preform long distance assessment. Andy