Though they’re known as sea lilies, crinoids are animals not plants. Think of them as starfish-on-a-stick: they are filter-feeding sea floor echinoderms, and relatively common as fossils go. Crinoids as a group aren’t extinct, but are relatively uncommon in modern oceans.
Here you can see the crown of Platycrinus saffordi, part of the Crawfordsville fauna of Indiana. This fauna is well known for its abundance of excellently preserved, articulated crinoid fossils, and contains at least 63 different species. This specimen lived sometime during the upper Lower Mississippian or upper Lower Carboniferous period, around 330.9 to 346.7 million years ago.
The stem is made up of stalked columnals, small coin-like structures. Most crinoid fossils are found with the stem and columnal in good condition, but fully fossilized crinoid crowns or heads (the tentacle-like thing you can see in the picture) are rare, as they tend to break apart after the animal dies and starts decomposing.