In the scheme of things, not to matter at all. Over time, the pressure within the Sun takes two simultaneous courses. One, the mass of the Sun shrinks to where the burning or conversion action slows down. The pressure has diminished, due to the reduced mass. As the Sun cools, its matter shrinks and compresses, a natural process known to humans.
Cold things are more dense than hot things.
This eventually sets off the second reaction of a dying star, the super nova or explosion. The Sun lights again, for one last time, this time in a violent and uncontrolled burn that sends its remaining particles off every which way.