Generally speaking, in the above assignment, does a subshell can be avoided using the following?

if [ -z "$FOO" ]; then if [ "$BAR" = "baz" ]; then FOO=true else FOO=false fi fi 

Yes, and that would be the correct way to write it.

: ${FOO:=$([ "$BAR" = "baz" ] && echo "true" || echo "false" )}

Runs a subshell (which is most shells involves the costly forking of a process) and is also wrong for several reasons:

• That ${FOO...} expansion is unquoted and therefore subject to split+glob, making it at least a DoS vulnerability (that's one of the examples given at Security implications of forgetting to quote a variable in bash/POSIX shells).
• echo "false" is run if either [ or echo true fails while you want it to be run when [ fails only. a && b || c is no proper substitute for if a; then b; else c; fi.

In the ksh93 shell, the subshell and those issues can be avoided with:

: "${FOO:=${ if [ "$VAR" = baz ]; then echo true else echo false fi }}" 

But that has little advantage over the standard and obvious if statement above.

Generally speaking, in the above assignment, does a subshell can be avoided using the following?

if [ -z "$FOO" ]; then if [ "$BAR" = "baz" ]; then FOO=true else FOO=false fi fi 

Yes, and that would be the correct way to write it.

: ${FOO:=$([ "$BAR" = "baz" ] && echo "true" || echo "false" )}

Runs a subshell (which in most shells involves the costly forking of a process) and is also wrong for several reasons:

• That ${FOO...} expansion is unquoted and therefore subject to split+glob, making it at least a DoS vulnerability (that's one of the examples given at Security implications of forgetting to quote a variable in bash/POSIX shells).
• echo "false" is run if either [ or echo true fails while you want it to be run when [ fails only. a && b || c is no proper substitute for if a; then b; else c; fi.

In the ksh93 shell, the subshell and those issues can be avoided with:

: "${FOO:=${ if [ "$VAR" = baz ]; then echo true else echo false fi }}" 

But that has little advantage over the standard and obvious if statement above.