What happens to a baby if their skull does not fully develop over the soft spots a year after they are born?

When a baby is born, it actually has several soft spots
all over the head - most are small enough though that they are virtually undetectable. 
"The" soft spot, the largest one right on top of the head, is the place where four bones
of the skull come together.  Typically, this soft spot does not
close by a year old.  Of course, every baby is different.  Some appear
closed as early as 9 months, others do not fully close until 2 years
old.

Most likely, the hypothetical child in your question
is developing completely normally.  The main area for concern with the skull in baby and
child development is in head growth.  At every checkup for the first 2 years of a
child's life, length, weight and head circumference are measured.  This is to make sure
the head is growing properly for brain development.  It would be more of a concern if
the soft spot closed very early and then the head was not growing at a normal
rate.

As for your question - the year old baby who still
has a soft spot is fine.  In fact, both my girls still had their soft spots and almost
no hair for the first year (one until 18 months) of their lives.