It may happen that a contact with an old iPhone can't save your vcard (.vcf) in his iPhone before iOS 13.
This is materialized by the fact that when he will launch the download of your card his iPhone will not offer to open the card in his contacts after clicking on "Save", but for example in "Files".
Whereas the iPhone should offer to open the card in "Contacts".
If your contact encounters this problem it is simply that he has deleted the "Contacts" application from his iPhone and will have to download it again.
To do this, he must go to his App Store and search for the "Contacts" application (direct link here from the iPhone), launch its download and open it
**You have to try again to download the Vcard.
Two scenarios:
1 / If the iPhone still offers Open in "Files" go to "Options" then search for "Copy to Contacts" the Vcard will open and you just have to click on "Save".
2 / If the iPhone proposes directly to Open in "Contacts" then click on it and once the Vcard is opened click on "Save".
You can check in the phone book if you can find the Vcard of the contact by looking for his name or the name of his company.