If you leave the Faroe Islands

Lapsing of permits
If a foreign national holding a residence permit leaves the Faroe Islands and remains outside the country for a long period, or gives up his residence in the Faroe Islands the permit lapses.
Although the applicant continuously keeps housing in the Faroe Islands at his disposal, regulations decide when a permit is lapsed due to the applicant´s stay outside of the country.
If a permit is lapsed the applicant has no right to stay in the Faroe Islands or to re-enter the country. If he/she wants to come back to the Faroe Islands he/she will need to apply for a new residence permit. .

If a foreign citizen holding a residence permit needs to stay outside of the Faroe Islands for a longer period of time he/she can apply for exemption in order to keep his residence permit in the Faroe Islands for his return to the country.
Further information on this can be found on the website of the Danish Immigration Service, see under "If you leave Denmark".