`cat archive.*tar |tar xvf - -g /dev/null --ignore-zeros -C destination`
At the end of tar files, is the 'end-of-archive' marker (2x 512 blocks of zero bytes. Tar will continue to read past the marker in some cases, but will not take any data.
`--ignore-zeroes` will tell it to keep reading regardless.
Related: Tar supports appending to archives; it does this by seeking to the end, rewinding two blocks, then continuing to write.