It depends on the country, facility and age of the foetus. In a hospital setting it’s almost always medical waste as far as I know, but some people choose burial or strew the ashes in a special place after an abortion/miscarriage. If it’s a medical abortion it’s a non-issue, usually flushed.

Stem cell research is based on controlled origins, such as embryos from IVF, scientific volunteering, egg donations or similar procedures.