I think there's no <MYPIPE> if open fails

Yes and no: the first <MYPIPE> does return undef, so the while loop never runs, but you should also be getting a warning "readline() on closed filehandle", indicating that something is wrong. A failed open doesn't have to be fatal, there are plenty of ways to handle the control flow:

if ( open my $fh, ... ) {
    while (<$fh>) { ... }
    close $fh;
}
else { warn "open: $!" }

# - or -

sub foo {
    open my $fh, ... or do { warn "open: $!"; return };
    while (<$fh>) { ... }
    close $fh;
}

# - or -

FILE: for my $file (@files) {
    open my $fh, ...
        or do { warn "skipping $file: $!"; next FILE };
    while (<$fh>) { ... }
    close $fh;
}

# - or -

use Try::Tiny;
try {
    open my $fh, ... or die $!;
    while (<$fh>) { ... }
    close $fh;
}
catch {
    warn "error: $_";
};
# same thing, but without the module:
eval {
    open my $fh, ... or die $!;
    ...
;1 } or do {
    warn "error: $@";
};
[download]

The fourth and fifth examples are different in that they catch any fatal error inside the block, which may or may not be desired.

Update: Added the third example, from this thread.