Yes, hard links will not break when a file is deleted. Because the file will remain to exist.
But a hard link to a file on a different file system is not possible, in a fundamental way.
Practically, that means you can not create hard links to files on different file systems, and get an error when trying.
Now, why is it not possible?
A hard link is what you normally call a file. When there is a file system mounted in
/mnt, and you see
/mnt/example.txt, you see the name of the hard link
example.txt on the file system in
/mnt, that points to the data of thee file.
A file system contains file data and file names to access parts of the data. There is a reference from the name to the data. This reference is a hard link.
Creating a hard link means to create a reference to the same file data with a new name.
So a hard link is a central part of a file system, referencing the data. That means that a hard link to a different file system is not possible - because it is a different file system.
In principle, there could be a file system that spans more than one partition, and enlarges when adding
/mnt to it. Then a hard link to a different partition, but in the same file system could be created, and would break when the partition with the data is unmounted.
With this reasons, it's not only that a hard link to a different file system can not be created, but that it can not even exist by definition.strong text