Hi Elizabeth,

That is a mealworm, the larvae of a darkling beetle (Family Tenebrioniidae). These beetles are known to feed on decaying organic matter, usually food or rotting wood. Your first goal should be to determine whether they are coming from inside or outside the home. Thoroughly inspect food stores, looking for signs of the beetle larvae, the adults, their frass and/or shed skins. Firewood stored in the home is another potential source. 

If there are no sources of decaying wood within the home, they are likely entering from outside through gaps along doors/windows/vents. If these gaps exist, small ones can be sealed with caulk. Larger ones may require professional servicing. 

To answer your question about reproduction, I have a theory as to why you are finding them dead in your basement. Mealworms prefer dark, damp environments which basements often create. The beetle larvae are likely feeding somewhere (e.g. food or rotting wood), and are attracted to the basement either because their food source has been exhausted, or they like the dark/moist conditions. Perhaps some beetle larvae successfully pupate, and the ones you are observing are the ones that failed to find the appropriate site before dying from desiccation. 

Let me know if you have further questions.