Given current situation that:
1) The defective account has email changed from original. But, via
some linking mechanism inside Google, it retains membership/ownership
of old groups (despite of new email address)
2) The old email address becomes unknown to Google. Signing up again
makes it new account to Google and has no membership/ownership to any
group.
Although the defective account cannot pass "Update Email Address"
page, note the first link under "Edit your Google-account addresses"
section. Following the link, it goes to the list of groups. Then,
for group that we have manager/owner privilege, there is a link next
to its name going to members management. We can add the original
email address back from there (either direct adding name, or use new
account of old address to request group joining and then use the
defective account to grant permission).