If you are worried that a subcontractor would copy-paste some existing code, I would be more worried that they would reuse code between clients. Just imagine the lawsuit where a for-profit competitor found out that your flagship product has code that they previously bought through the some developer.
Subcontractors should always spell out that some parts of the delivered project will use MIT licenced code, or code licenced to the subcontracting company itself.
Personally, when I do business development and two companies end up co-authoring a library (like say a new plugin), we always specify what parts of the new library are for the company we helped write the plugin, and what parts are "ours".
Sometimes we'll write a bit and say "this is yours, we'll never use it again", and sometimes we'll say "we wrote this, you can use it, but we're free to give it to anyone else too".
