Files located in
/var are very much system-critical. For example,
/var/spool/mail contains the users' email; you would no more delete that than you would light a fire in your neighbor's mailbox. It's only files in certain subdirectories of
/var that contain files that are more or less transitory: log files in
/var/log, caches that can usually be recreated in
/var/cache, temporary files (which you should not delete while they're in use!) in
/var/lib can be quite critical. For example, MySQL is usually configured to store its databases in
/var/lib/mysql by default: if you erase that, you wipe your databases. Dpkg puts its own databases under
/var/lib as well;
/var/lib/dpkg/status is one.
/var/lib/dpkg/status contains information about installed packages. If you've erased that, you should restore it from a backup. If your backup isn't fully up-to-date, check the logs of recent package manipulations under
/var/log/apt and in
/var/log/dpkg.log. You'll need to create that file before
dpkg will work.
/var/lib/dpkg/available is built from data downloaded from the Internet.
apt-get update should rebuild it.
/var/lib/dpkg/info contains files that ship with Debian packages. You can restore these files simply by reinstalling the packages. Of course, you will need a list of installed packages for that. If you've restored
/var/lib/dpkg/status, then you can extract the list of packages from there.
apt-get install --reinstall $(</var/lib/dpkg/status sed -n 's/^Package://p')
If you've lost
/var/lib/dpkg/status, then you may be able to recreate it by creating an empty file, then running
apt-get install --reinstall on the list of packages. One place where the list of packages is also saved is
/var/lib/apt/extended_states, at least if you've only ever used APT to install packages (as opposed to
dpkg directly) — use that file instead of
/var/lib/dpkg/status int the command above. If you've deleted that too, you can rebuild an approximate list of packages with
$(cd /usr/share/doc && ls), because most packages create an entry in
/usr/share/doc. There are probably a few exceptions.
Do not ask for any assistance about package management on this system. Recovering from the deletion of system-critical files is not an exact science. If you can't restore from backups, you should install a new, clean system as soon as possible.