This week, the island of Samoa is switching time zones, causing it to skip from Thursday directly to Saturday. Out of simple curiosity, what implications might this have on any Jews on the island? Since one cannot "jump" into the middle of Shabbat, does that mean all observant Jews would have to leave the island?
The civil date line doesn't affect the Halachic day with regards to Shabbos.
Where is the location date line is subject to Halachic argument
According to the Chazon Ish, the Halachic dateline hugs the coast of Australia, China and Russia. Anything to the east (Japan, etc) is considered to be on the same day as the United States. Therefore, it's Shabbos in Japan on their Sunday.
Samoa used to have Shabbos on Saturday (like Hawaii). Now it will be pushed off a day (to be like) Japan and have it on Sunday.
According to R' Tukachinsky, the halachic date line is between Hawaii and California. Therefore, Hawaii is on the Japanese side and Shabbos is on their Friday.
Samoa used to have Shabbos on Friday (like Hawaii). Now it will be pushed off a day to Saturday.
There are other opinions that it runs straight through the middle of the Pacific, though there are arguments of exactly where does it run.
The question of where the Halachic International Dateline is is its own independent question. The decision in Samoa would only matter if we left date-line issues to governmental/secular authorities, which is not the case. The day to keep Shabbos in Samoa would be seven days from the last time it was to be kept, according to which ever opinion we should/do go by.
It seems The Star K picked up on the question: How to Keep This Shabbos in Samoa? STAR-K Tells Us How (Samoa & Tokelau To Cross International Date Line)