Babies are usually not aborted after 12 weeks (depending on local laws) unless there is a major emergency such as disease, accident or threat to life.
The babies who die during miscarriages or full-term labour are usually cremated or buried with funeral rights. However parents could choose to donate the organs and blood if they wished. A woman could choose to donate the umbilical cord and placenta for stem cell research. Would depend on type of hospital or clinic.