It appears there's an entire blog post that addresses this completely here.
Here is an excerpt of the blog, which describes the plot line of the characters within this book written by Mark Verheiden (non-canon):
Aliens: Book One picks up with Newt as a disturbed young woman plagued
by nightmares of Acheron. As we meet her, she is confined to a mental
institution. Similarly, Hicks is also disturbed by his memories of
LV426. He is shunned by his peers, who deride and accuse him of being
infected with some alien disease. This one-time “rock of Gibraltar”
and cool-headed Corporal now lives as a pariah, prone to drunkenness
and outbursts of frustration. The overall story concerns Earthly
interest in obtaining an Alien as a bio-weapon. Hicks is recruited to
train a squad of Marines to take on an apparent Alien threat, though
this is really a ruse by a Dr. Orona to obtain samples. Meanwhile,
Newt’s doctors decide that her nightmares and outbursts are too
extreme to handle and plan to lobotomise her.
And the blog even described the first script written for the film's screenplay, which was rejected by the producers:
In the first Alien III script, by cyberpunk author William Gibson, the
Sulaco still drifts through space with its sleeping cargo (it doesn’t
seem like anyone gets home on time in this series.) The ship enters
the territory of the Union of Progressive Peoples (essentially,
communists) and is boarded. Inside, Ripley, Newt, and Hicks are still
in stasis. Bishop’s cryotube however is home to an Alien egg, which is
nestled within his entrails. The U.P.P. take Bishop’s body and send
the Sulaco back into drift, where it eventually comes into contact
with the Company. Now boarded by Marines, Ripley’s cryotube is damaged
in a firefight between the soldiers and a spontaneously appearing
Alien (later, a restored Bishop simply states that the Alien Queen
“somehow deposited genetic material on the ship.”)
Throughout Gibson’s Alien III, Ripley’s life hangs precariously in the
balance, Newt is shipped off to her grandparents on Earth early on,
and Hicks slugs on as the protagonist along with Bishop, with both
striving to keep the out-of-commission Ripley alive whilst
concurrently battling an Alien threat. Producers David Giler and
Walter Hill liked Gibson’s script, but were unhappy that the author
had not “opened up” the story further in his two drafts. This
dissatisfaction, and with the end of the Cold War relegating the plot
to an anachronism, saw the script being booted. The next script kept
the concept of a male lead but scrapped any notion of Hicks, Newt,
Bishop, or Ripley returning.
And thanks to Richard's comment below:
It might interest you to know that Foster originally planned to have
Newt survive the crash (in the novelisation). He was told by the
studio that under no circumstances was he even allowed to imply it.
They saw her death as an essential event. - Richard