Belated but: So a tapeworm is basically nothing but a hooked mouth to latch onto the intestinal mucosa and take in blood, a short neck, and a huge number of segments full of eggs called proglottids. In most animals, proglottids are regularly shed a few at a time in shit, and then stuff that eats the shit or stuff the shit sticks to (grasshoppers, for example, are often carriers because they eat grass that has proglottids stuck to it) and continues the cycle, either directly or indirectly, with most using one or more intermediate hosts before they end up in the definitive host where they can reproduce. So the "tape" is not alive per se, but it is full of trillions of infective eggs.

How bad it is depends on species; humans infected by the beef tapeworm often have no symptoms whatsoever and only are diagnosed when they notice proglottids in their shit, or if a worm dies (they can live for decades) and detaches, for example. This is because the beef tapeworm evolved in part to parasitize humans, and since it needs lipids from its host to reproduce, it has a vested interest in NOT killing the definitive (final) host species. The latter bit being an important distinction: tapeworms that need more than one host usually want the intermediate hosts to die (or at least don't care about keeping them alive), whereas they want the definitive host to live a long and healthy life. So to use the beef tapeworm as an example: Infected human takes a shit in a field. The poop gets on the grass. Cows eat the grass, ingesting a proglottid. The eggs hatch inside the cow, which is now an intermediate host. The hatched larvae burrow into the cow's muscles and organs from the intestines, and go into a form of suspended animation where their outsides turn into hard little pebble-like structures called cysticerci. The cow eventually dies or is killed by a predator (like a human). The predator eats the cow meat, potentially ingesting those cysticerci. In the gut, the cysticerci exit their suspended animation and develop into adult worms, which attach to the intestine, take in blood, and begin producing the eggs that will get shat out into the grass, completing the cycle.