Well, DEB packages are extractable!
So, you can simply download the DEB package, extract it, take the binary from it and place it where it should be inside your system (this is visible from the DEB's structure, anyway).
For example, let's say that you're missing a binary file.
Download the DEB package using this script:
URI=$(apt-cache show $PACKAGE | grep "Filename:" | cut -f 2 -d " ")
It takes as argument the package.
Then, you extract the package and you will see a
usr folder and inside it a
bin folder (this is usually where the binary package is being installed). So, you copy this binary file to
/usr/bin and you are done.
Be careful NOT to download later versions of the package than the one that you had installed in your system in order to avoid incompatibility problems!
EDIT: After a constructive comment by chaos please note that if you have already installed the package in your system then you can find it in
/var/cache/apt/archives/. Taking the package from there is a good idea, because you can be sure about the incompatibility issues.