You need to ask whether the tension is set ok, and if there is any way of changing the tension ie could you use a pair of pliers to turn what's left of the button.
You need to try out the machine with a piece of spare fabric to test the tension. The tension is how the top and bottom threads relate to each other. If the tension is too high or low then the stitches won't be evenly balanced. Hopefully the tension will be ok, otherwise there are sewing machine shops who can service and repair the machine.
Thanks for the replies, I'll ask her everything you've advised me to find out when she drops it off. I don't know what make it is at the moment but when it gets here I'll do some research to see if its worth fixing (I'll probably end up coming back here to ask you all ). All I know is its an old machine she has had for years.