Within the last week, on two different occasions, had two mice wander to the center of my basement floor while I was walking around. Both were slow and eventually died. Absolutely no poison in our basement. What could be causing this?

Depending on where you live, mice may have been poisoned somewhere else. Mice are scavengers but always return to their nest. You may want to have an exterminator check to see if you have any mice nesting in your home. May be one of your neighbors has rat poison in or around their home.

Unless there's a predator near your house that they escaped from after an injury, that's the most likely explanation.

Finding where they're getting in and blocking off the entrance would seem to be your next step.