Good in terms of what? If the forum is the entire site, sure let it have its own domain. However, if the forum is part of a site/blog, adding on a "community" aspect, a subdomain or subdirectory is preferable, imo, just to be on the same main domain as the main site.
A subdomain is classed as a different domain. So you will lose rankings, serps, etc.
You can permanently 301 redirect forum.example.com to forumexample.com but that will not help other than redirect your visitors/members to the new domain.
You would need to ask those that linkback to you to update their links so they point to forumexample.com instead of forum.example.com.
Or you could leave the page forum.example.com up with some info about where the new site is and include link to new site ( forumexample.com ) on the same page. That way pr goes to forum.example.com and pr from forum.example.com goes to forumexample.com.
Probably best not to change it now.
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