US passport holders are eligible for a visit visa on arrival. It is illegal for anyone other than the person who is named in the passport to hold it no matter what their nationality. The passport is the property of the government that issued it.
Exit permits are issued by employers/sponsors upon request and are not supposed to be withheld except in very specific circumstances. If the sponsor agrees, a multiple exit permit can be applied for that is good for one year. The holder can exit at will.