Just another set of examples to drive home the point that, whatever else may happen (i.e., with the newlines), the  * (asterisk) is always gone:

c:\@Work\Perl\monks>perl -wMstrict -le
"my $s = qq{AAA*\n};
 ;;
 my $t = $s;
 print qq{A1: '$t'};
 $t =~ s/\*$//;
 print qq{A2: '$t'};
 ;;
 $t = $s;
 print qq{B1: '$t'};
 $t =~ s/\*\s$//;
 print qq{B2: '$t'};
 ;;
 $t = $s;
 print qq{C1: '$t'};
 $t =~ s/\*[\n]$//;
 print qq{C2: '$t'};
"
A1: 'AAA*
'
A2: 'AAA
'
B1: 'AAA*
'
B2: 'AAA'
C1: 'AAA*
'
C2: 'AAA'
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Note that:  \n is a member of the  \s (whitespace) set;  [\n] is the same as  \n (newline) alone. Please see perlre, perlretut, and perlrequick.

Update:

Does perl let you print $line as a literal string with \n etc.?

Some questions can be answered by simple experimentation. What happens when you print the strings "foobar", "foo\nbar", "foo\n\n\nbar", "foobar\n", "foobar\n\n\n", etc?