The Remington 870 has been around since 1950, and all possible "bugs" are long since worked out.
UNLESS the gun's trigger unit is defective (or more likely) someone has been inside it altering it for a "better" trigger pull, these are as safe as a shotgun can be.
There are two ways an 870 can fire ACCIDENTALLY, and BOTH require the chamber to be loaded.
1. The hammer must drop. Either by "accidentally" pulling the trigger or by a defective trigger assembly failing and allowing the hammer to drop from a jar or bump.
2. The gun must be dropped squarely on the muzzle from a great height, (like off a building's roof).
The 870 firing pin (like all shotguns) is an inertial type in which the firing pin is shorter then the hole in the bolt, and has a strong spring holding it back.
Since the pin is shorter than the hole, the firing pin cannot touch the primer, and MUST be driven forward with enough force to overcome the spring and still hit the primer with enough force to fire it.
IF the gun's chamber was loaded, and IF it was dropped from a great height, and IF it hit squarely on the muzzle, the gun's firing pin MIGHT be driven forward by inertia and MIGHT fire the shell.
(A LOT of if's, and might's).
In fact, the Remington 870 Police model is VERY safe.
The trigger assembly has an extra strong trigger/sear spring to make it harder to accidentally pull the trigger, OR allow the hammer to bump or jar off and fire it.
The firing pin spring is strong, and a the only way the gun could fire inside a patrol car would be IF, the chamber was loaded, and IF the gun was carried with the barrel down, and IF the car was driven off a cliff. Hitting a "bump in the road" won't do it.
So, if you buy a Remington Police Model 870 shotgun and carry it in what is known as "Cruiser ready" condition (magazine loaded, chamber EMPTY), the gun CANNOT fire.
All that's needed to get the gun ready to fire, is to pump the action, chambering a round.
Hundreds of thousands of police carry Remington shotguns this way with NO trouble ever recorded.
Were there are "accidents" these are always traced to people doing things they were specifically trained NOT to do.
Specifically chambering a round, then inadvertently pulling the trigger.
These are always explained away as "some kind of freak accident".
Bottom line: Buy a Remington 870 Police Model, keep the magazine loaded, and the chamber empty, until you need it.
INFO on new Remington Police models:
Remington applies a sprayed-on coating of mil-spec cosmoline at the factory, both inside and out.
This is to preserve the gun during shipping and possible long-term storage.
After buying a new Police gun, the cosmoline will rub off, and is often mistaken for RUST, since it's a reddish color.
The gun WILL rust if not properly treated since cosmoline is a STORAGE grease ONLY.
Remington recommends disassembling the gun, including the magazine tube, and spraying the entire gun dripping wet, inside and out with a cleaner-lube like Rem-Oil or CLP Breakfree.
Allow to soak for 15-20 minutes to dissolve the cosmoline and allow the new lube to soak into the finish, then wipe off the excess and assemble the gun.