Yesterday at my club's Three-gun match, we were discussing the differences between the new and old style Remington 870 Shell Lifters. The new style lifter came out around 1985-86, around the same time as the Rem-Choke system. The newer style had a three-sided, rectangular cut-out in it. This was known as the Flexi-Tab Shell Lifter. Remington also made changes to the Bolt and the Carrier Plate to accommodate the new lifter.
The reason for the changes was because Remington received complaints that if you Short-shucked an 870, or didn't fully seat the shells into the magazine tube, a shell could inadvertently pop out under the bolt, and on top of the lifter, which would jam up the shotgun. The old style Lifter was made of heavier material so it was far more rigid and wouldn't flex. Now if you loaded an 870 properly and didn't Short-shuck the action this wasn't a problem. I've owned and used several (old type) Remington 870's since around 1975 and I've never experienced this problem. I currently have five of the old style 870 police shotguns in my inventory.
Now if you do experience a jam of this nature there are a couple ways of clearing it. You can take a pocket knife and slide it along the Shell Lifter, pushing the round back into the magazine tube (another reason to always carry a knife). Or you can hold the Slide Release lever in and strike the butt of the shotgun on a hard surface like the ground (muzzle pointed in a safe direction of course) and that should clear the jam. If I was fighting for my life, and I had cover available to me, this would be the technique I'd use.
Now Remington sells a conversion kit consisting of a new Bolt, Shell Carrier, and Carrier Plate. Depending on where you find them, the update kit runs from $65.00 to $99.00. Either Brownell's or Midway USA probably carry this conversion kit. Personally, if you have an old style 870, I'd say save the money and use it towards shotgun ammo so you can learn how to run the gun properly.
Of course, if you do experience a jam on any long gun and you don't have available cover, then you should be transitioning to your handgun. Now if you're carrying a long gun into a armed encounter and you don't have a handgun to transition to, then you've just stepped into another pile of dog dung.