Thanks for the help everyone, I've also found you can write it like this as well:

while ( <code goes here> ) {}
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The important but being that there's nothing in the {}. This gives us the original one-liner broken up to this:

#!/usr/bin/perl
my $string = 'abc abc abc \textit{abc abc} abc \textit{abc abc \textbf
+{abc \textbf{abc abc} abc} abc} abc.';

while ($string =~ s/\\text(i|b)[tf]\{([^{}]*)\}/<$1>$2<\/$1>/g) {}
print $string;
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Or you could take out the {} and add a 0, X, or whatever in front of the while (...)