**Core Concept**
The fibrous band in question is a peritoneal fold that plays a crucial role in the support and positioning of abdominal organs, specifically the liver. This structure is a remnant of the embryological development of the liver and is essential for maintaining the liver's normal anatomical position.

**Why the Correct Answer is Right**
The fibrous band described is the ligamentum venosum, which is a fibrous remnant of the ductus venosum. During fetal development, the ductus venosum is a shunt that connects the umbilical vein to the inferior vena cava, allowing for the bypass of oxygenated blood from the placenta to the fetus's liver. After birth, the ductus venosum closes and eventually becomes the ligamentum venosum, which attaches to the inferior vena cava and the left branch of the portal vein.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the ligamentum teres hepatis (round ligament of the liver) is a fibrous remnant of the umbilical vein, not the ductus venosum.
**Option B:** This option is incorrect because the falciform ligament is a peritoneal fold that attaches the liver to the anterior abdominal wall, but it is not attached to the inferior vena cava or the portal vein.
**Option C:** This option is incorrect because the coronary ligament is a peritoneal fold that attaches the liver to the diaphragm, but it does not attach to the inferior vena cava or the portal vein.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the ligamentum venosum is a fibrous remnant of the ductus venosum, which closes after birth. This knowledge can help you identify the correct anatomical structure in various clinical scenarios.

**Correct Answer: C. The ligamentum venosum.**