If notification is set up properly, every time an issue is assigned to a new individual, an email notification is sent to that individual to inform them that they have been assigned ownership. (see note for special case)
There is also a notify list in the details of every bug. All members of this list will also be sent notification of any change that is made. There is an optional Server Configuration setting which places the creator of the issue in this notify list whenever a new issue is raised. In this way, the creator can track all changes to any issue that they raise.