I'm assuming you want all of the copied files to wind up in the same place.
It sounds you want all of the files in /path/to/$work where the filename starts with a line from the boards file to be copied to some destination.
eg., given
$ cat boards
start1
start2
$ ls $work
start1.txt
start1.jpg
start2.txt
start2.jpg
start3.txt
$
you want start1.txt, start1.jpg, start2.txt, and start2.jpg to be copied to somewhere, but not start3.txt.
Don't use xargs: it's a fantastic tool, but it's going to cause problems if any of your files or "search patterns" have spaces or glob characters (eg., "*").
Rather, use a tool that expects a search pattern, find.
cat boards | while read pattern
find $work -name "${pattern}*" -exec cp {} /path/to/destination +
done
That will read in each line of boards as a search pattern. find will then look in the $work directory to find files (and folders!) that match ${pattern}*; each found item (file or folder) will be passed to cp as a properly-escaped parameter (in the {} spot), and it will do xargs-like minimization of the number of cp processes it starts because of the + (if you wanted exactly one process per found item, you'd use a ; instead - be sure to escape it properly, though).
find has a rich set of filters you can apply to narrow down your search. Of particular note is the -type f option which will limit the results to file.
Note that the cp command may fail if there are folders in the argument list passed in from find; using the -type f filter will prevent that.
Note also that the cp command will "flatten" the output directory - if $work has subdirectories which happen to have matching files, those files will be copied straight to /path/to/destination. If you want to only copy files at the top level of $work, the -maxdepth filter (probably with a value of 1: -maxdepth 1) will prevent find from recursing too deep down the file system.
Note also that find is case-sensitive. If you don't want it to be, you can use -iname instead of -name to do a case-insensitive search.
If there are any other command line parameters you want to give cp, just put them in front of the {} (eg., cp -r {} to copy directories that match the search pattern).