Bash – Single command to login to SSH and run program

The most obvious way to run a command remotely is to specify it on the ssh command line. The ssh command is always interpreted by the remote user's shell.

ssh bob@example.com '. ~/.profile; command_that_needs_environment_variables'
ssh -t bob@example.com '. ~/.profile; exec zsh'

Shared accounts are generally a bad idea; if at all possible, get separate accounts for every user. If you're stuck with a shared account, you can make an alias:

ssh -t shared-account@example.com 'HOME=~/bob; . ~/.profile; exec zsh'

If you use public key authentication (again, recommended), you can define per-key commands in ~/.ssh/authorized_keys. See this answer for more explanations. Edit the line for your key in ~/.ssh/authorized_keys on the server (all on one line):

command="HOME=$HOME/bob;
     if [ -n \"$SSH_ORIGINAL_COMMAND\" ]; then
       eval \"$SSH_ORIGINAL_COMMAND\";
     else exec \"$SHELL\"; fi" ssh-rsa AAAA…== bob@some.where

The best way to do this would be to use pam.

In /etc/pam.d you will have several files, one of them will be called sshd. If you only want to affect ssh, and not other logins (such as a GUI, or real TTY), you want this file.
If you want to affect all logins, you'll want a 'common' file. The name of this other 'common' file varies by distro, but you can track it down by following the include and substack statements in the sshd file until you get to the base file.

Once you've identified the file in /etc/pam.d that you want to use, add a line such as the following to the session section:

session     optional    pam_exec.so quiet /etc/pam_session.sh

This will result in calling /etc/pam_session.sh every time someone logs in and logs out (whether gracefully or ungracefully).

Now you just need to create /etc/pam_session.sh. Below is an example you could use to run something every time someone logs out:

#!/bin/sh
if [ "$PAM_TYPE" = "close_session" ]; then
  something
fi

(don't forget to chmod a+x the script)