Users using live feed are able to search and add inactive users even though they normally can't see these user records outside of live feed
This is because live feed is querying for user records in live_profile table and not sys_user table. The inactive users still have corresponding live_profile records.
Either of the following resolution options can be considered:
1) Delete the unneeded live_profile record for the inactive user
2) Write a before query business rule on live_profile to only return records where the corresponding sys_user records are active
There is an out-of-the-box query business rule called "user query" that restricts inactive users from being returned for non-admin. Since live feed does not actually query for sys_user table (and instead in live_profile) this business rule does not apply as such.