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#PHP, 133 bytes a PHP port of @edc65´s JavaScript port of DLosc´s Pip answer.

function f($s){for(;$c=lcowbe[$i];)$a[$c]=substr_count($s,$c)>>!$i++;return min($a);}for($s=$argv[1];f($s)==f($s.=$s[$i++]););echo$s;

takes lower case input from command line argument. Run with -nr.

breakdown

// function to count the cowbells:
function f($s)
{
    for(;$c=lcowbe[$i];)            # loop through "cowbel" characters
        $a[$c]=substr_count($s,$c)  # count occurences in $s
            >>!$i++;                # divide by 2 if character is "l" (first position)
        return min($a);             # return minimum value
}
for($s=$argv[1];    # copy input to $s, loop:
    f($s)               # 1. count cowbells in $s
    ==                  # 3. keep looping while cowbell counts are equal
    f($s.=$s[$i++])     # 2. append $i-th character of $s to $s, count cowbells
;);
echo$s;             # print $s