A few comments:

• The file handle "F" has package scope and actually would be known in the subroutine without passing it as a parameter. I recommend using lexically scoped "my" variables for filehandles as I show below.
• If for some reason the subroutine needs to know the line that "triggered its being called", just pass that line to the sub as I also show. There are complicated ways to "re-read" and otherwise deal with "backing up one line" on a filehandle, but usually the best way is to just tell the subroutine that line as a parameter so that nothing complicated is required. In general once you read a line from a filehandle, use it as soon as a possible, or save it, but don't "back-up" in the input stream of lines from the filehandle.
• I show the standard idiom for a while{} loop that reads a filehandle. The loop typically ends when the file contains no more lines. It is not necessary to check for eof. Under some circumstances, you may need while(defined ($line = <$fh>)){} to prevent a warning message.
• Your code is not clear with @ref. I passed a reference to that array that the subroutine modifies.
• I opened a file handle to a memory variable. I did that to produce a single runable Perl program file.

#!/usr/bin/perl
use strict;
use warnings;

my $text=<<END;
This is an example test file
that has xyz
line following the matching line
2nd line after the matching line
END

open my $fh, '<', \$text or die "unable to open text $!";

my @array;

while (my $line =<$fh>)
{
   SubOut($fh, \@array, $line) if $line =~ /xyz/;
}
close $fh;

print @array;


sub SubOut
{
   my ($fh,$array_ref, $match_line) = @_;
   
   push @$array_ref, $match_line;
   
   while (my $s_line = <$fh>)
   {
       print "$s_line";   
   }
}
__END__
Prints:
line following the matching line
2nd line after the matching line
that has xyz <--- this is in @array
[download]

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