As with the OP's version that you based yours on, this fails several of these tests:

my @tests = (
    # $string, $pos, $expected, $description
    [ "\nString\n", 2, 6, 'Surrounded' ],
    [ "String\n",   2, 6, 'No first \n' ],
    [ "\nString",   2, 6, 'No last \n' ],
    [ "String",     2, 6, 'No \n' ],
    [ "",           0, 0, 'Blank' ],
);
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Since the OP's version failed those as well, this is understandable. Obviously even more tests would be needed, but this was meant as more of a sanity check than anything.

Performance-wise, here's where your solution fits in:

                Rate     op_ver      daxim    rlindex cur_strlen
op_ver      564186/s         --       -23%       -66%       -86%
daxim       737063/s        31%         --       -56%       -81% <-- H
+ERE
rlindex    1677856/s       197%       128%         --       -57%
cur_strlen 3932672/s       597%       434%       134%         --
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Of course, I am not sure what sort of performance impact (for better or worse) a fixed version of your code would have. Complete code for my test and benchmark suite is in my comment, if you want to have a go with it yourself.

not ok 1 - daxim: Surrounded
#   Failed test 'daxim: Surrounded'
#   at /home/ryan/src/perlmonks/subline.pl line 37.
#          got: '7'
#     expected: '6'
Use of uninitialized value $prev in subtraction (-) at /home/ryan/src/
+perlmonks/subline.pl line 64.
not ok 2 - daxim: No first \n
#   Failed test 'daxim: No first \n'
#   at /home/ryan/src/perlmonks/subline.pl line 37.
#          got: '7'
#     expected: '6'
Use of uninitialized value $prev in subtraction (-) at /home/ryan/src/
+perlmonks/subline.pl line 64.
not ok 3 - daxim: No last \n
#   Failed test 'daxim: No last \n'
#   at /home/ryan/src/perlmonks/subline.pl line 37.
#          got: '1'
#     expected: '6'
Use of uninitialized value $prev in subtraction (-) at /home/ryan/src/
+perlmonks/subline.pl line 64.
Use of uninitialized value $next in subtraction (-) at /home/ryan/src/
+perlmonks/subline.pl line 64.
not ok 4 - daxim: No \n
#   Failed test 'daxim: No \n'
#   at /home/ryan/src/perlmonks/subline.pl line 37.
#          got: '0'
#     expected: '6'
Use of uninitialized value $prev in subtraction (-) at /home/ryan/src/
+perlmonks/subline.pl line 64.
Use of uninitialized value $next in subtraction (-) at /home/ryan/src/
+perlmonks/subline.pl line 64.
ok 5 - daxim: Blank
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