Does qpopper supports IPv6?

In short: no.
In long: you can patch the latest qpopper with patch available here to support IPv6. In FreeBSD if you enable IPv6 with WITH_IPV6 options globbally in /etc/make.conf, then all your packages compiled from ports comes with IPv6 support, including qpopper.

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- * In long: you can patch the latest [ftp://ftp.qualcomm.com/eudora/servers/unix/popper/ qpopper] with patch available [http://www.imasy.or.jp/~ume/ipv6/qpopper4.0.9-ipv6-20060626.diff.gz here] to support IPv6.  In FreeBSD if you enable IPv6 with {{{WITH_IPV6}}} options globbally in {{{/etc/make.conf}}}, then all your packages compiled from ports comes with IPv6 support, including qpopper.
+ * In long: you can patch the latest [[ftp://ftp.qualcomm.com/eudora/servers/unix/popper/|qpopper]] with patch available [[http://www.imasy.or.jp/~ume/ipv6/qpopper4.0.9-ipv6-20060626.diff.gz|here]] to support IPv6.  In FreeBSD if you enable IPv6 with {{{WITH_IPV6}}} options globbally in {{{/etc/make.conf}}}, then all your packages compiled from ports comes with IPv6 support, including qpopper.