My tooth crown fell out but not the root

Hi:The root of the tooth will decay but may not fall out since it is supported by bone.  It’s best to have the root removed before it decays.Best,Dr. Maddahi

No, the root is going to collect food particles around the gum causing gum infection. It might also get infected at the end of the root(Apex). You need to see a dentist to remove the root asap.

Hello!
In answer to your question, yes, if you don't do something about it soon, the root will also suffer decay, but this time it wont just fall out, it could cause infections and pain, however you are still in time to get some xrays taken and verify if it is still possible to do a root canal and maybe even place a new crown with a post.
Hope this helps, good luck