MyBB Community Forums

MyBB home is
http://localhost/mybb

In Full mode link is:
http://localhost/mybb/member.php?action=profile&uid=1

In Lite (Archive) Mode:
http://localhost/member.php?action=profile&uid=1

Subdirectory path is lost and we got 404 error.

MyBB Version 1.4.4

This is reproducible.

I can reproduce this too.

Should be

http://localhost/forums/mybb/mybb14x/public/mysql/member.php?action=profile&uid=1

Is

http://localhost/forums/mybb/mybb14x/public/member.php?action=profile&uid=1

I'm 99.9% sure this was already reported and fixed for 1.4.5

Yes it was fixed in this thread:
[F] Bad profile link in archive mode, SEO off