Here’s my take on the requirement (and, admittedly, it’s only a guess): Identify sentences containing the target string 23456 and delete them, leaving the other sentences — together with their surrounding markup — unchanged.

I came up with this algorithm:

1. Slurp the input file in as a single string.
2. Extract sentences:
1. Remove markup tags.
2. Extract each “sentence” as a minimal sequence of characters beginning either at the beginning of the string or following the whitespace at the end of the previous sentence, and terminated by a full stop, a question mark, or an exclamation mark, which is in turn followed either by whitespace or by the end of the string.
3. Filter out sentences which do not contain the target string.
4. Delete the remaining sentences (i.e., those which do contain the target string) from the original input string, thus leaving the original markup unaffected.

The trickiest part of this is identifying sentences. Here’s my solution:

#! perl
use strict;
use warnings;

my    $original  =  do { local $/; <DATA>; };
my    $string    =  $original =~ s{ <  /? (?: p | br) > }{}grx;
my    @sentences =  $string   =~ m{ ( .*? (?: [.?!] \s+ | \z) ) }gsx;
chomp @sentences;
      $original  =~ s{$_}{} for grep { /23456/ } @sentences;
      $original  =~ s{ +}{ }g;
print $original;

__DATA__
<p>Find more business news at facebook.com and twitter.com. Text BUSIN
+ESS to 
23456 for breaking business news text alerts on your mobile phone. Tex
+t JOBS to 23456 for job alerts.</p>
<p>Want your news even faster? Text NEWS to 23456 to sign up for break
+ing news text alerts. See for a complete list of alerts.</p>
<br>SIGN UP FOR MOBILE NEWS ALERTS! Get your news on the go, text NEWS
+ to 23456
[download]

Output:

16:49 >perl 1326_SoPW.pl
<p>Find more business news at facebook.com and twitter.com. </p>
<p>Want your news even faster? See for a complete list of alerts.</p>
<br>SIGN UP FOR MOBILE NEWS ALERTS!

16:49 >
[download]

Hope that helps,