The second situation would be zombie reaping. If the process spawns child processes and does not properly reap them it will lead to a full process table

When a process loses its parent, init becomes its new parent. init periodically executes the wait system call to reap any zombies with init as parent.

Zombie processes should not be confused with orphan processes: an orphan process is a process that is still executing, but whose parent has died. When the parent dies, the orphaned child process is adopted by init (process ID 1). When orphan processes die, they do not remain as zombie processes; instead, they are waited on by init.

The result is that a process that is both a zombie and an orphan will be reaped automatically.

The term zombie process derives from the common definition of zombie — an undead person. In the term's metaphor, the child process has "died" but has not yet been "reaped". Also, unlike normal processes, the kill command has no effect on a zombie process.

This occurs for the child processes, where the entry is still needed to allow the parent process to read its child's exit status: once the exit status is read via the wait system call, the zombie's entry is removed from the process table and it is said to be "reaped".

When a zombie is created (i.e. which happens when its parent exits, and therefore all chances of it ever being waited by it are gone), it is reparent to init, which is expected to reap it (which means calling wait on it).

In other words, someone has to clean up after "irresponsible" parents that leave their children un-wait'ed, and that's PID 1's job.

Have lost their parent (i.e. their parent exited as well), which means they'll never be waited on by their parent.

Now, unlike other processes, PID 1 has a unique responsibility, which is to reap zombie processes.

According to the Unix process model, the init process -- PID 1 -- inherits all orphaned child processes and must reap them. Most Docker containers do not have an init process that does this correctly. As a result, their containers become filled with zombie processes over time.

In a Unix-like operating system any orphaned process will be immediately adopted by an implementation-defined system process: the kernel sets the parent to this process

Let's look at a concrete example. Suppose that your container contains a web server that runs a CGI script that's written in bash. The CGI script calls grep. Then the web server decides that the CGI script is taking too long and kills the script, but grep is not affected and keeps running. When grep finishes, it becomes a zombie and is adopted by the PID 1 (the web server). The web server doesn't know about grep, so it doesn't reap it, and the grep zombie stays in the system.

The rsync and sleep commands (the sleep is just an example) are run through exec to prevent the creation of zombie processes if I kill the parent script while they're running, and each potentially-long-running command is wrapped in its own subshell so that when exec finishes, it won't terminate the whole script.