"I seriously doubt she just rocked up to cambridge, one of the biggest cities in the country for inequality, and expected to be housed."
Based on my professional experience, a surprising number of people actually do this. They arrive in Cambridge with no local connection and then seek housing advice, complaining that private renting is unaffordable and wanting social housing. Of course the list is very long even for people who meet the local connection criteria.
There is a housing crisis in Cambridge (and throughout the UK) but people in vulnerable situations are often not well informed and don't always make decisions that others might see as rational or logical.