Here's a variation based on index that seems to satisfy your requirement insofar as I understand it as discussed here, here and here.

Note that this solution is O(n1 * n2) (the product of the number of lines in each file) because it depends on a nested loop, whereas the regex-based solution presented by BillKSmith here is O(n). Unfortunately, the regex-based solution imposes a tighter limit on the size of the substrings file that can be supported: at least several hundred, but surely no more than several thousand substring lines. The index-based solution, while potentially much slower, can support a few, perhaps several, million lines of substrings. (Caveat: These are all estimates.) The number of lines to be searched for substrings is unlimited with both approaches if the lines are processed line-by-line in a while-loop. The code below identifies both lines that match some substring and lines that do not match any substring, so comment out whichever branch of the if-else conditional you do not need. (There's also a bit of ornamental code that highlights the substring that was found.)

c:\@Work\Perl\monks>perl
use strict;
use warnings;

use autodie;

use List::MoreUtils qw(any);  # use List::Util in later perl versions

my $file1 = \<<"END1";  # strings to be searched for substrings
he is man
xyzzy
don't you
what goes on
END1

my $file2 = \<<"END2";  # substrings to search for
he is
what are
z
try to do
END2

open my $fh_substrings, '<', $file2;
my @substrings = <$fh_substrings>;
chomp @substrings;
close $fh_substrings;

open my $fh_lines, '<', $file1;

while (my $line = <$fh_lines>) {

    chomp $line;

    print "'$line' ";

    my $s;  # matched substring in line
    my $o;  # matched substring offset

    if (any { ($s = $_, $o = index($line, $_)) >= 0 } @substrings) {
        print "match \n";
        print ' ', ' ' x $o, '^' x length $s, "\n";
        }
    else {
        print "NO match \n";
        }

    }

close $fh_lines;

__END__
'he is man' match
 ^^^^^
'xyzzy' match
   ^
'don't you' NO match
'what goes on' NO match
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