What will new employer do if they receive bad (maybe anonymous) email about you (perhaps from your ex employer)? What can you do ?
Technically, I don't see the context where they can do anything.
(Speaking from the U.S. standpoint) Employers are very restricted in the types of information they can exchange with other employers about employees.
If the email is anonymous, then the source cannot be verified and the information cannot be considered reliable. They can't do anything with it.
If the email is not anonymous and can be traced back to the former employer, you can sue the pants off of your former employer and if your new employer acts on the information, you can sue the pants off of them too.
That said, if the experience puts a really bad taste in their mouth, it will probably put strain on your employment, and they will quickly be able to create a different unrelated circumstance that puts your employment at risk.
You should provide more context and detail.