to check whether a member of deleted group still has access to the SQL server, run the following:
exec xp_logininfo 'DOMAIN\user','all'
most probably, if it does have, then it should be via another AD groups on the server
to get group members of existing AD group, run the following:
exec xp_logininfo 'DOMAIN\Group','members'
moreover, it's possible to get list of AD groups in a domain:
EXEC xp_enumgroups 'DOMAIN'