On my system, man -2 stat enumerates

EACCES

Search permission is denied for one of the directories in the path prefix of path. (See also path_resolution(2).)

EBADF

filedes is bad.

EFAULT

Bad address.

ELOOP

Too many symbolic links encountered while traversing the path.

ENAMETOOLONG

File name too long.

ENOENT

A component of the path path does not exist, or the path is an empty string.

ENOMEM

Out of memory (i.e. kernel memory).

ENOTDIR

A component of the path is not a directory.

And I don't see anything there for read failures (incl communication failures with remote volumes).

perl -MErrno=ENOENT -le'
   $found = -e shift;
   die("stat: $!\n") if !defined($found) && $! != ENOENT;
   print($found ? "found" : "not found");
' file
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