do demultiplexers remember
Decoders don't remember, but addressable latches and shift registers do.  A 74HC259 will work much like a demultiplexer, but outputs which are not selected will retain their current state unless or until they are selected.  A 74HC595 shift register has two sets of eight flip flops; clocking the first set ("shift clock") will cause the first flop to capture the state of the data input while the second captures the former state of the first, the third captures the former state of the second, etc.  The state of the eighth will appear on an output pin where it can be connected to the data input of another chip.  Clocking the second set of latches ("register clock") will cause the contents of the first eight to be copied to the second eight.

Using addressable latches, it's easy to set up a system to allow individual bits to be changed directly without having to reload everything.  Using shift registers, it's possible to control an arbitrary number of outputs using only three pins ("data in", "shift clock" and "register clock") but changing any output will require reloading all of them.