She obviously likes to have cash in a safe. Could it be black money? That would explain the behaviour.
I heard that before from one of my uncles. Having black earned money is not that much fun, because you can only spend it abroad. In our country all big transactions are reported, so you can't just buy a new car cash without anyone noticing it.
If this is not the case, sould your mother be told that it is much more expensive to pay bills at the bank instead of via internetbanking? At least here in Norway it is and it is only elderly people who still like to pay their bills in cash at the bank. They pay like 5 $ extra for each transaction.