Not sure if there is some payment entitlement difference between resigning and being sacked. However two things strike me:
a) the employer might be trying to do your friend a favour as he/she can say they resigned rather than was fired in any future job interview
b) if he/she resigns, they will probably not be able to claim unfair dismissal in any future squabble, although they might be able to claim constructive dismissal.
However it very much depends on whether the case is cut and dried or not, if it is then option a) might be the more charitable opinion to take.