How to copy between servers files that have changed more than X days ago?

Question

Backup

There is a task to make a backup of backups - to protect their backups from overwriting with zeros, encryption by malware, and deletion. To do this, I think to raise a "slave" backup server with a lag of 3-7 days, which itself will connect to the main one and take files that have changed more than X days ago. Is there a way to make rsync work like this?
Well, or if someone has more reasonable thoughts on how best to arrange it - I will be glad to hear =)
Thanks for the good ideas.

Answer 1

Installed urbackup on another network. Set up clients. I look at the pictures and rejoice.