Does this tenant have shorthold tenancy by default?

Tenancy Types and Management

A couple renting a room in one of my houses.
The man was renting the room, his girlfriend became pregnant, he then left and she has no money/work etc.,
She is Polish and has no entitlement to benefits.
It would seem that there are hundreds of people in this situation causing massive social problems.
This is by no means an isolated problem. I often have people renting rooms or houses that are unable to pay their rent. They run up debts with local authorities, gas and electricity etc, then leave the property and this usually has to be cleared up. Thousands of pounds must be owed in areas similar to ours. Costing the Government a lot of money.