You can use $(!!) to recompute (not re-use) the output of the last command.

The !! on its own executes the last command.

$ echo pierre
pierre
$ echo my name is $(!!)
echo my name is $(echo pierre)
my name is pierre

The answer is no. Bash doesn't allocate any output to any parameter or any block on its memory. Also, you are only allowed to access Bash by its allowed interface operations. Bash's private data is not accessible unless you hack it.

Very Simple Solution

One that I've used for years.

Script (add to your .bashrc or .bash_profile)

# capture the output of a command so it can be retrieved with ret
cap () { tee /tmp/capture.out; }

# return the output of the most recent command that was captured by cap
ret () { cat /tmp/capture.out; }

Usage

$ find . -name 'filename' | cap
/path/to/filename

$ ret
/path/to/filename

I tend to add | cap to the end of all of my commands. This way when I find I want to do text processing on the output of a slow running command I can always retrieve it with ret.

One way of doing that is by using trap DEBUG:

f() { bash -c "$BASH_COMMAND" >& /tmp/out.log; }
trap 'f' DEBUG

Now most recently executed command's stdout and stderr will be available in /tmp/out.log

Only downside is that it will execute a command twice: once to redirect output and error to /tmp/out.log and once normally. Probably there is some way to prevent this behavior as well.