When I run...
perlbrew switch perl-5.16.0
...I get...
A sub-shell is launched with perl-5.16.0 as the activated perl. Run 'exit' to finish it.
...then a bash prompt appears.
Is this expected behavior? If not, how can I fix it?
That happens when you have an improperly installed perlbrew. As part of the installation, you are instructed to add a command to your shell startup script, but that appears to be missing.
Add the following to your shell startup script:
source .../perlbrew/etc/bashrc
There's a similar script for csh.
source .../perlbrew/etc/cshrc