now that you show the actual data, I would just get the nums from the end of the lines via match global, thusly:

use strict;
use warnings;

my $str = 'Adam Knowles|||https://www.site.com/?ID=11977|||11977~~~Ale
+x Burleson|||https://www.site.com/?ID=27627|||27627~~~Billy|||https:/
+/www.site.com/?ID=18836|||18836~~~Billy|||https://www.site.com/?ID=18
+836|||18836~~~Christopher Duarte|||https://www.site.com/?ID=14713|||1
+4713~~~Dave Martin|||https://www.site.com/?ID=5590|||5590~~~Drew Ruba
+do|||https://www.site.com/?ID=26867|||26867~~~Emily Hanson|||https://
+www.site.com/?ID=6782|||6782~~~James Gehrke|||https://www.site.com/?I
+D=7834|||7834~~~Jeff Banta|||https://www.site.com/?ID=11446|||11446~~
+~Jeffrey P Sandoval|||https://www.site.com/?ID=14637|||14637~~~Jesse 
+Bollinger|||https://www.site.com/?ID=8034|||8034~~~Jonathan Walker|||
+https://www.site.com/?ID=4811|||4811~~~Jordan Hall|||https://www.site
+.com/?ID=12549|||12549~~~Joseph Dodds|||https://www.site.com/?ID=2621
+1|||26211~~~Mark Tappan|||https://www.site.com/?ID=5370|||5370~~~Mary
+ Christine Hammill-Perkins|||https://www.site.com/?ID=15901|||15901~~
+~Mary E. Boesch|||https://www.site.com/?ID=20326|||20326~~~Matthew Sm
+ith|||https://www.site.com/?ID=26752|||26752~~~Matthew Tuggle|||https
+://www.site.com/?ID=13170|||13170~~~Moises Cariaso|||https://www.site
+.com/?ID=27397|||27397~~~Nicole Masciola|||https://www.site.com/?ID=2
+7230|||27230~~~Paul Zenns|||https://www.site.com/?ID=8396|||8396~~~Pa
+ul Zenns|||https://www.site.com/?ID=8396|||8396~~~Phillip Scott|||htt
+ps://www.site.com/?ID=5015|||5015~~~Ross Martin|||https://www.site.co
+m/?ID=27192|||27192~~~Sam Lavine|||https://www.site.com/?ID=26277|||2
+6277~~~Stephen Beatty Jr|||https://www.site.com/?ID=10557|||10557~~~T
+ODD A PARTIN|||https://www.site.com/?ID=21876|||21876~~~';

my @favnums = $str =~ /\|\|\|(\d+)~/g;

$#favnums = 24 if ($#favnums >24); #maximum of 25 fav's

my $favnumstr = join ",",@favnums;
print $favnumstr;

11977,27627,18836,18836,14713,5590,26867,6782,7834,11446,14637,8034,48
+11,12549,26211,5370,15901,20326,26752,13170,27397,27230,8396,8396,501
+5
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