library(xts)
timeXts <- xts(1, as.POSIXct("2000-01-01"))
dateXts <- xts(1, as.Date("2000-01-01"))
xts:::index.xts(timeXts)
# [1] "2000-01-01 CET"
xts:::index.xts(timeXts[0,])
# integer(0)
xts:::index.xts(dateXts)
# [1] "2000-01-01"
xts:::index.xts(dateXts[0,])
# Date of length 0

library(zoo)
timeZoo <- zoo(1, as.POSIXct("2000-01-01"))
dateZoo <- zoo(1, as.Date("2000-01-01"))
zoo::index(timeZoo)
# [1] "2000-01-01 CET"
zoo::index(timeZoo[0,])
# POSIXct of length 0
zoo::index(dateZoo)
# [1] "2000-01-01"
zoo::index(dateZoo[0,])
# Date of length 0

> sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.3 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale:
 [1] LC_CTYPE=en_GB.UTF-8          LC_NUMERIC=C                 
 [3] LC_TIME=en_GB.UTF-8           LC_COLLATE=en_GB.UTF-8       
 [5] LC_MONETARY=en_GB.UTF-8       LC_MESSAGES=en_GB.UTF-8      
 [7] LC_PAPER=en_GB.UTF-8          LC_NAME=en_GB.UTF-8          
 [9] LC_ADDRESS=en_GB.UTF-8        LC_TELEPHONE=en_GB.UTF-8     
[11] LC_MEASUREMENT=en_GB.UTF-8    LC_IDENTIFICATION=en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] xts_0.12.1.2 zoo_1.8-9    rj_4.0.4-2  

loaded via a namespace (and not attached):
[1] compiler_3.6.3  tools_3.6.3     rj.gd_4.0.4-2   grid_3.6.3     
[5] lattice_0.20-41