Welcome to Perl and the Monastery! The best thing to do is not use regexes to try to parse HTML. Here, I'm using Mojo::DOM, which is modern and fairly easy to use:

#!/usr/bin/env perl
use warnings;
use strict;
use Mojo::DOM;

my $filename = 'C:/Users/li/data_collection/posts/165644996453.html';

# slurp the whole file into memory
open my $fh, '<', $filename or die $!;
my $html = do { local $/; <$fh> };
close $fh;

my $dom = Mojo::DOM->new($html);
my $text = $dom->find('footer')->last->previous->text;
print $text,"\n";  # prints "indeed I am"
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The problem you're probably having with the regex in your solution is that while (<FILE>) is only reading one line at a time, but to match over multiple lines, you need to read multiple lines (or the whole file) into memory.

Update: Just to make clear what's going on in that my $html line: $dom->find('footer') returns a list of <footer> elements (probably only one?), ->last picks the last one of those, ->previous goes one node back to the <p> element, and ->text gets the text content of that element.