1860 Russell Co VA Census # 1416Judith Fraley38 FSeamstress$10____ Duff04 M____ Patsy Burriss53 FSpinner____
This census image definitely shows Patsy instead of Betsy.The enumerator may have mis-heard the name since they do sound so much alike.
1870 Russell Co VA Census (Castlewood, Enum. Aug 4, 1870) # 41Judy Fraley48 FWeavingVA Elizabeth BURROWS60 FDomestic WorkNC Sidney BURROWS18 FSpinningVA
1870 Russell Co VA Census (Castlewood, Enum. Aug. 5, 1870) # 109Judy Fraley45 F Keeping HouseVA Duffer16 M Farm HandVA Betsey BURROWS60 F WeaverVA
The two 1870 Russell Co VA Census listings above for the Judy Fraley household shows that Elizabeth Francis was indeed the "Patsy" shown in the 1860 census.So, best guess is that she was either really Martha Elizabeth Francis OR she was nicknamed Betsey and the census enumerator just messed up.