You can feed each of the 16 outputs from decoder to the Clock input of 16 individual T-FlipFlops (positive edge-triggered). Connect all T-inputs to '1' (Vdd) permanently.
When any of the decoder outputs goes 0 -> 1, the bit in the T flip-flop will toggle (assume it is '0' initially).
Now, for eg., when the decoder o/p becomes 0001_0000_0000_0000, device number 4 is switched ON. It will remain ON unless the same decoder output arrives again (because T flip-flop will toggle only for a 0 to 1 transition at its clock input).
So if the decoder output goes to (say) 0000_0010_0000_0000 in next cycle, device number 4 remains unaffected (ON) and simultaneously device 7 also turns ON.
The limitation here will be that you will be applying same 4-bit input code to turn it ON/OFF.. so you'll need some mechanism to keep track which device is ON and which one is OFF. I think you may put some LEDs in parallel at each flip-flop output (for user convenience).