Problem Description
An operating system design flaw that has persisted over about three years is the presence of program running, using memory, and slowing down the computer after they have been closed and quit. This has been reported to Apple, and others have noticed it as well, but the problem remains through the current macOS Sierra Version 10.12.2 release of the Apple operating system.
Reproducing the Problem
To reproduce the problem described above, at the end of a day or two of use, close all your programs, then press Option+Command+Esc to bring up the Force Quit menu (similar to Task Manager in Windows) to view that the programs are still running. The Dock area should show all program icons, and those that are running should have a black dot under them. See the screen shot below.
Temporary Workaround Fix
Using the Force Quit menu (Option+Command+Esc) highlight the programs that no longer appear to be running in the Dock and then choose force quit. See the screen shot below.
Screen Shot
Below is a screen shot showing this issue. Programs can be seen in the Force Quit dialog, but they are not indicated as running in the Dock (as shown by a black dot under the icon for the running programs). In the example below, Numbers, Preview, and Text Edit are shown as still running after they have been closed and quit.
