How do I get the last word in each line with bash

Try

$ awk 'NF>1{print $NF}' file
example.
line.
file.

To get the result in one line as in your example, try:

{
    sub(/\./, ",", $NF)
    str = str$NF
}
END { print str }

output:

$ awk -f script.awk file
example, line, file, 

Pure bash:

$ while read line; do [ -z "$line" ] && continue ;echo ${line##* }; done < file
example.
line.
file.