$* reflects the args passed to the function, but you didn't pass any! You merely passed some to bash as you executed the bash command untouchable. You want to execute the bash command untouchable john mike bill, which you can do using

system(q{bash -ic 'untouchable john mike bill'});
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or better yet,

system('bash', '-ic', 'untouchable john mike bill');
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The latter launches bash directly instead of launching a sh to launch bash.

If the names are variable, you want:

use String::ShellQuote qw( shell_quote );
system('bash', '-ic', shell_quote('untouchable', @names));
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or

system('bash', '-ic', 'untouchable "$@"', '-', @names);
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If I run untouchable from the command line, it works as expected.

But running the command you passed to system wouldn't have.