You say they gave notice to quit - was this in line with their AST? Had they come to the end of a fixed term or were they in a periodic tenancy (i.e. gone past the fixed term and not signed a new agreement)?
If they have left the property during a fixed term or without keeping to the terms of the AST then the Landlord can withhold the deposit in lieu of the missing rent.
If, on the other hand, they have done it strictly by the rules and left at the end of the fixed term or by giving at least a months notice ending on a rent day if in a periodic tenancy, then they probably have justification in requesting the deposit back. It really depends on these factors.
When did the tenancy start, how long for, when did they leave, what notice did they give and, yes, was the deposit protected?