Hello Kwon, I see you listed in SalesForce and am copying my teammate @Namsoo Kim so he can work directly with you.
Generally speaking filesystems should never become full, they usually auto expand - so your environments should be revisited. If/when a filesystem become full, it will not fail, but incoming writes from client will fail, but reads will not.
I suggest working with Namsoo and opening a case if your customer experiences an issue (beyond the fact that client writes fail).