You have stem cells through out your entire life, you might be confusing (adult) stem cells with embryonic stem cells.

Adult stem cells can turn into only a limited type of cells. Embryonic stem cells can turn into any type of cells.

Your bone marrow contains adult stem cells mainly haematopoietic stem cells which can turn into various other sells like erythrocytes (red blood cells) and lymphocyte (white blood cells).

The stem cells are mobilized from the patient's marrow using a mobilizing agent such as cyclophosphamide, which allows the cells to be collected from the patient's blood.

The adult bone marrow has stem cells at various stages of maturation that are involved with producing the cells of the blood.

Stem cells are readily available from adult fat tissue.