I hate to disagree with @meditrina but I am going to on this specific point..
Technically, only a regular admissions year (reception, year 3 in some schools, year 7) has a PAN. Often other years are referred to as having a PAN, but unless they are an admissions year, it is a notional not an actual PAN.
Infant Class Size is a different situation, there is no leeway, but above that admissions authorities do have leeway to admit over the notional "PAN" for that year - a year 3 class of 30, say, could have 31 if the admissions authority chose to take an extra child, which they are allowed to do.
(They can also decide to admit over actual admissions PAN in a regular admissions year if they want - this year a number of schools local to me did in Yr7 in agreement with the LA as it's a bulge year. What they can't do is admit under PAN if there are children wanting the spaces; and children over PAN have to come from the waiting list in order)
However, the extra child would have to be the next child on the waiting list; they can't just choose who to take. So if OP is not top of the waiting list, the school can't just decide she should have a place because they feel sorry for her situation. If she is, they could, but in reality, this doesn't often happen, as it annoys another local school by taking a child away from them, and usually local schools like to keep on good terms. Schools prefer to be able to say, "the appeals panel made the decision, not us!"