Joint tenancy and one party has served notice

Other

I have a property let to two people on an AST. The term has ended and it has become periodic. the notice period is 1 month.

I believe that the couple have split up. One of them has just served notice to leave.

My questions are:

1. Does this notice by only one party serve as notice for both parties or do they both need to serve notice separately.
2. If the party that has served notice leaves at the end of the notice period, but the other party still wants to stay at the property what then happens? is this party liable for the whole of the rent or only half?

Thank you for your assistance.

Kind regards

David.