reserved blocks. for ext4 you can see the current settings with sudo tune2fs -l <device>, it's called Reserved block count
Something like tune2fs -r <count> <device> to change the number of reserved blocks. A default format on ext4 will be 5%.
I do not remember the equivalent command for xfs, but I'm reasonably confident there is a 1:1 equivalent.
Note also that this isn't a true 1:1 to the OP, because root can write to reserved blocks, but that's kind of the point behind it: normal processes can't completely fill the disk and prevent root from doing admin tasks.
Unless those normal processes run as root, of course. Not that that ever happens.
I think the idea is that once you are low on space, you can reduce the percentage of reserved blocks