You can use the more advanced deluser command:

sudo deluser --remove-home user

You can also try the the --remove-all-files option. From man deluser:

By  default,  deluser  will  remove  the user without removing the home
directory, the mail spool  or any other files on the  system  owned  by
the  user.  Removing  the home directory and mail spool can be achieved
using the --remove-home option.

The --remove-all-files option removes all files on the system owned  by
the  user.  Note  that  if you activate both options --remove-home will
have no effect because all files including the home directory and  mail
spool are already covered by the --remove-all-files option.

As can be expected, the second option may take a while to complete.

Option 1:

Use the deluser command.

However, before doing so check the file /etc/deluser.conf

And check the line

# Remove home directory and mail spool when user is removed
REMOVE_HOME = 0

Ensure this to 0 (not 1) before calling deluser.

Option 2:

sudo vipw Find the entry you want to remove (first part of the line up to the first ':' is the username). Then type "dd" to remove the entire line.

Save and exit with "esc + wq".

From man usermod

-d, --home HOME_DIR

The user's new login directory.

If the old home didn't matter, the new home probably also wouldn't matter, but you could use something like /var/nonexistent to show that the home directory is not needed or supposed to exist.