Is there a way they actually track this? Because I wouldn't be at all surprised for lots of cards clearly written by shakey-hand old people to mysteriously disappear and chalked up as a "senior moment" that they forgot to send it.
Depenfs of the countries, but in France, sending cash through the mail is actually illegal, and although the Post won't seize it, they also won't care if its stolen.
Cheques are the safest option, and gift cards are covered by postal insurance if stolen, but consider mailed cash as gone before it hits the mailbox.
For the US (and there's likely very similar systems and even better of course systems elsewhere) there are options with tracking and extra protections can be added for the lower classes of mail such as receipts, tracking, insurance, etc.
The standard a shakey-hand old person might use in the US is First Class Mail (It's the US, so of course the fancy name denotes the lowest retail tier) which is not trackable without paying, but by US law is sealed against inspection (giant asterisk, but historically the Inspector General's Office is known as even more grimly attached to their task than the IRS) which does offer some reassurance.
A postman messing with the mail is a felony crime that hits so hard in federal court, you don't get many morons risking it a year. The Feds love easy cases to pad their numbers, they would metaphorically pillory the fuck out of a rogue postman.
EDIT: The US postal service also sells "Postal Money Orders" which can be exchanged at any post office or any retail business offering postal services for cash. That's an inexpensive option that my grandma-in-law uses to stuff her cards.
This is entirely correct. But the example I'm thinking of though is the low hanging fruit, didn't do anything to protect against fraud and has very probably been the victim of scams previously.
"Here's my big pile of Christmas cards Mr. Postman" straight from the front door and one or two of those just happen to not make it. Or the person doing the pickup from a drop box or whatever they're called.
It's the sort of spontaneous, in the moment, thing that could come up a fair number of times and that I can imagine someone getting away with as long as they don't push it too many times per season. And the sort of thing I would hope the people in charge of not letting that happen have a plan against.