Hand and Foot Rules on playing all cards without going out
I've never played this game but have read the at rules here. they say

To 'Go Out', the player must get a Clean and Dirty, and get completely
rid of the cards. Players must discard the final card, and not 'simply
run out of cards'.

So to me this reads if you have 'simply run out of cards' then you have not 'gone out'.   It also suggests that having a Clean and Dirty book is a requirement for going out so even if you have no cards but not the required books you have not 'gone out'
You would continue to play as normal until you had the required Clean and Dirty books or another player 'goes out'