eshell-delete-exited-processes

eshell-delete-exited-processes is a variable defined in `esh-proc.el'.
Its value is

t

Documentation:
If nil, process entries will stick around until `jobs' is run.
This variable sets the buffer-local value of `delete-exited-processes'
in Eshell buffers.

This variable causes Eshell to mimic the behavior of bash when set to
nil. It allows the user to view the exit status of a completed subjob
(process) at their leisure, because the process entry remains in
memory until the user examines it using M-x list-processes.

Otherwise, if `eshell-done-messages-in-minibuffer' is nil, and this
variable is set to t, the only indication the user will have that a
subjob is done is that it will no longer appear in the
M-x list-processes\ display.

Note that Eshell will have to be restarted for a change in this
variable's value to take effect.

You can customize this variable.