it depends, i think. i would support the member who is going solo only if i've been a fan of theirs (and their music) during the time they were in a group. if i don't really like the member, then i think i'd rather support the group instead.
besides for KAT-TUN, i was never in this situation before (i've only been listening to boybands for 2 years, and none of my rock bands lost a member) so it's hard to tell. overall, i guess it just depends