I think things depend on how the market is going and whether the parties are in a position to service a potentially long term debt - e.g. bridging finance. Even if they could organise it , are they comfortable with the idea that their own house may not sell for a while?
In reality, the optimum way to deal with the situation is to sell their current house, pocket the money, rent somewhere ( not easy for short term) and as soon as purchase new place. There is a risk that prices will shoot up ( a trifle unlikely!) and there is the inconvenience of moving twice. It is however preferable to possibly being stuck with two properties.
mf