To answer your question - if you do test positive while in the BVI (on Day 0, Day 4 or exit test) it is a mandatory minimum 14 day quarantine in your accommodations. Then you need to have a negative PCR test to be released.

In some cases where the accommodation has been booked by someone else during those 14 days, alternative arrangements have been made. Moved from a villa to boat, or into a hotel, etc.