Generally speaking, that is often exactly what happens. If there is one weekly rotation, the crew stay for a week then operate the next home bound schedule. A destination such as Cuba has a number of resort airports and it isn't unusual for crews to be also bussed from one resort to another to operate an inbound schedule that results in less than a week stopover. Similarly and depending on the area of operation, crews can be "airlined" from one destination to another.
It can be a complex process of costing that depends on the season and subsequent availability of resource, but certainly stopping over for a week is often the cheapest option for an airline and it is not at all unusual.