How can a state case ""jump the fence"" into the federal court system?

By Diversity Jurisdiction

Explanation:

Cases that are based on state law may be brought to a federal court under the court's "diversity jurisdiction."

This occurs in a situation where the plaintiff and defendant live in different states. The plaintiff can file a case in a federal court when the defendant live in another state.

The defendant can also seek to move to a Federal Court for the Same reason.

Note that Criminal cases do not fall under diversity jurisdiction and the amount in dispute must be more than $75000.