Evidence from the USA says it can happen
According to Wikipedia:
Death following live birth caused by abortion is given the ICD-10 underlying cause description code of P96.4; data are identified as either fetus or newborn. Between 1999 and 2013, in the U.S., the CDC recorded 531 such deaths for newborns, approximately 4 per 100,000 abortions.
Induced labour without explicit feticide is sometimes practiced in Europe
Europe's abortion rules says that "12 weeks" is the usual limit for most countries, but up to 24 weeks in the United Kingdom.
How an abortion is carried out (by the NHS in the UK) says,
Late abortion (20-24 weeks)
There are two options for a late abortion carried out at 20-24 weeks.
Both require an overnight stay in hospital and are described below.
Surgical two-stage abortion – stage one stops the heartbeat of the foetus and softens the cervix. Stage two is carried out the following
day and involves removing the foetus and surrounding tissue. Both
stages are carried out under general anaesthetic.
Medically induced abortion – this is similar to a late natural miscarriage and involves the medicine, prostaglandin, being injected
into your womb, making it contract strongly (as in labour).
Contractions can last six to 12 hours. You will remain awake during
the procedure and will be given medicines to help control the pain if
needed. D&E may then be used to ensure the womb is completely empty.
The latter procedure doesn't do anything to specifically kill the fetus, therefore it can result in "live birth".
At 20 weeks the fetus weighs 10 oz (300 g) and is 7" (18 cm) long.
Week Twenty: The halfway point
Your baby now weighes about 11 ounces and at roughly 7 inches long they are filling up more and more of the womb. Though still small and fragile, the baby is growing rapidly and could possibly survive if born at this stage.
Apparently, in the UK the fetus is not considered a separate person until after it is born.
The Law Lords concurred that a fetus, although protected by the law in a number of ways, is legally not a separate person from its mother in English law.
The BBC reports that live births happen in practice
A 2007 article titled One in 30 aborted foetuses lives says,
One in 30 foetuses aborted for medical reasons is born alive, a 10-year study at 20 UK hospitals has found.
Most of these babies with disabilities were born between 20 and 24 weeks of pregnancy and all lived for no more than a few hours.
The article continues,
Safeguards
Usually, the foetus will not survive the procedure.
The Royal College of Obstetricians and Gynaecologists said it had
"very strong" guidelines on terminations of pregnancy after 22 weeks.
According to the guidelines, after 22 weeks and beyond, if there are
signs of major foetal abnormality and the patient has requested an
abortion, the patient should be offered feticide, where a lethal
injection is administered.
The patient has every right to refuse this course of action. If the
baby is born alive, palliative care should be provided till the baby
dies.
Theoretically, such an event could result in a doctor being accused of
murder if a "deliberate act" - that is, legal abortion - were to be
followed by a live birth and the subsequent death of the child because
of immaturity.
The article concludes,
"It would be wrong to imply from this retrospective study, that if
women undergo a medical induction abortion at under 24 weeks'
gestation for reasons aside from foetal abnormality, that this is at
all likely to result in a live birth.
"Doctors working in abortion care have for some years now followed the
Royal College of Obstetricians and Gynaecologist's guidance, that the
foetal heart is stopped before a medical induction abortion around 22
weeks' gestation."
She added: "To end a wanted pregnancy because of severe foetal
impairment is, understandably, a very difficult choice for women and
couples."
A spokeswoman from the charity Antenatal results and Choices said:
"Feticide is technically demanding and stressful for parents and
professionals alike.
"Enforcing the procedure in cases where death is the inevitable
outcome either as a means to reduce apparent perinatal mortality
figures or to satisfy those who do not support the legal availability
of abortion will not benefit anyone."