Unfortunately there is nothing InfinityFree can do about this, it’s a potential problem that can occur on any subdomain, no matter who the provider is.
Connecting a custom domain is the best way to prevent this from happening in the future, but you can use a different free subdomain if you wish.
My recommendation is to add the custom domain as a parked domain, it will then share the same files, no migration necessary (Unless you run software like WP, then you’ll need to change the site URL).
If you want to add a subdomain, follow this guide to take a copy of your files, then follow it in reverse to upload them to the new domain.