When can they be sent out?
A Final rejection is sent out when the examiner decides that the examination should not continue any longer or if a rejection remains after the applicant replies to the second Office action. It basically serves to indicate "You're out!" in the patent rejection system. Applicants have a limited amount of time to respond to the Final rejection. If they choose not to respond, then the application will be abandoned.

It should be noted that a Final rejection may be sent out as a first, second or final Office action. For example, if the examiner receives a ridiculous patent claiming an invention that is already common knowledge (there is nothing new about it), then a Final rejection might just be sent out right away. Examiners will not go through the motions of an examination when it is blatantly obvious that the application will never, ever stand to gain a patent. It might seem a little harsh, but that's the way it goes.

What to do?  
After the Final rejection has been sent out, the applicant will usually have three months from its mailing date to send in an appropriate reply or the application will be abandoned. The possibilities for replying after a Final rejection include the following three options.

The first is that the applicant may file a Notice of Appeal. When a Final rejection is appealed, the application will be reviewed by the Patent Trial and Appeal Board. This Board will decide whether the examiner was correct in rejecting the application or they will overrule the examiner's rejection and allow the claim(s).

The second option is to file a response that places the application in condition for allowance. This may be done by canceling certain claims or by making the amendments that were suggested by the examiner.

Lastly, the applicant may file a Request for Continued Examination (RCE). In order to file an RCE, a bona fide attempt at advancing the examination must be included. The PTO won't tolerate just dredging things along for no good reason.