Hi Cindy & Juan,
This may not be the case with Stephen Burwell, but it is very possible that-like many other Franklin County men-he went to work in the West Virginia mines. I have many examples in my family history wherein the husband would leave the family for work in the mines of McDowell, Mercer, Wyoming & Raleigh counties, in particular. They would return to Franklin County when bad weather would not permit mine work. Somtimes the whole family would temporarily relocate to WV. I have evidence of some Franklin County relatives with children born in both Virginia and West Virginia.
I found the 1900 census for the Burwells in Gills Creek, Franklin County, Va. Emma is listed as Mary E. Burwell, married. Children include Elisa, James & Lewis. Stephen is not listed, and so far I cannot find him elsewhere. The marriage record for Stephen lists his bride as Mary Emma Tyree.
Try using Burrell and Banwell as you continue to search. I'll keep in touch if I find anything else.