'Household member' relationship type can't be (re?)activated through the interface?
Do you have any extensions that might have disabled it? Otherwise I'm not sure how that would happen either but if you want to live on the edge you can use phpmyadmin or equivalent to do:

UPDATE civicrm_relationship_type SET is_active=1 WHERE name_a_b = 'Household Member of';

You can also do it with api explorer (/civicrm/api3) and choose:

Entity: RelationshipType

Action: Create (yes, create - it means update)

Remove the suggested parameters and add a parameter Relationship Type ID = 8. You can confirm the id by hovering over the View link in the Relationship Types listing screen and looking at the url at the bottom of the browser, but it's always 8.

Then add a parameter Relationship type is Active = Yes

Click Execute.