It is the third type Flobert action, known as the "rolling block."
This is an insult to Remington because it was nowhere nearly as sturdy as even the smallest true Remington Rolling Block.
As you can see by the breechblock having blown clear off.
There are no parts available and you would be horrified at the cost to have a breechblock made, probably hundreds of dollars. The only hope would be to buy a worse junker of the same type to salvage the part off of.
And it STILL would not be strong and safe enough to shoot with smokeless ammunition.