Depending on where your saffron was grown and harvested, it could be perfectly normal to have the yellow style still attached or it could be the first sign that your saffron isn't quite up to snuff.
Iran - Saffron from Iran, the largest producer of saffron in the world, is very thin and small in size and there are two basic varieties.
One contains only the red stigma with absolutely no yellow style; whereas the other comes with the full style attached to the stigma and tied in a bunch of several hundred.

This Table shows only a selection of the most important countries of origin and should not be thought of as exhaustive.

Europe Spain, Greece, Italy, France, Russia, Portugal
Africa North Africa
Asia Iran, India, Pakistan, China, Japan
America USA (Pennsylvania)
Australia

Unfortunately, there is nothing to stop saffron producers from making their saffron with only half true stigmas and the other half made up of the yellow styles. There's also nothing to prevent them from dying these yellow styles red to give the appearance of quality saffron.
Now if you come across saffron that seems too good to be true - it's all red and very inexpensive - you're probably dealing with inferior saffron.
Remember to look for the ISO certification, which all quality saffron will have. But if you bring it home and you're still not so sure, here's a quick test. When you first put quality saffron in liquid, the liquid will turn a slightly pale yellow, and over time will turn the liquid a stronger and more vibrant color.
If your saffron immediately turns the water a strong yellow, this is a sign your saffron was artificially colored. What you are actually seeing is the dye washing off your saffron.

Saffron is produced from the dried, yellowish orange 2.5 - 4 cm long stigmas of the purple-flowered saffron crocus. The stigmas are in the form of tubes which open out at the top into a funnel shape. It is the most valuable, most expensive spice in the world.

Harvesting saffron is very labor-intensive: each blossom has three stigmas, which are picked by hand in the morning, before the heat of the day, and then dried for 15 - 30 minutes. The blossoms are thrown away.

The term spice is used to refer to plant parts which serve to improve the odor and flavor of foods. They contain essential oils and other ingredients which have a strong seasoning action.

Spices are processed, cleaned, graded and carefully packaged for overseas dispatch in the countries where they are cultivated. They are dried to preserve them for transport and storage. In consumer countries, they are delivered to spice mills, where they are cleaned and graded again, ready for sale in ungrounded or ground form.

Saffron has an aromatic, hot and slightly bitter taste. Saffron contains a water-soluble coloring matter known as croc in, which provides a golden-colored dye which is effective even at a dilution of 1:100,000.

1 kg of saffron represents 100,000 to 200,000 blossoms, the stigmas of which have to be removed by hand, which explain the high price and the frequent cases of adulteration with parts of other plants and other organic or inorganic substances.

Saffron is very light-sensitive and hygroscopic and must therefore be well sealed and protected from light during transport. The product is therefore packaged in cans which are in turn packaged in boxes. Sometimes saffron is packaged in corrugated board cartons lined with aluminum.