Bifurcation is the “special election” for PR BFRs described on page 9 of IRS publication 570. Essentially, for non-PR-source assets you sell as a BFR-PR, you can choose for the unrealized gains up until the date you established BFR-PR to be non-PR-sourced and taxed by the IRS, and gains afterwards up until the date of sale to be PR-sourced and treated under PR tax law.
If not voluntarily chosen, all gains from non-PR-sourced assets will be taxed by the IRS unless the sale happens after you have been a BFR-PR for 10 years, at which point the 10-year securities rule applies and the assets are PR-sourced, the IRS has no claim to them, and the rate is 5%. The bifurcation rule is an election, not a requirement, so if you are in a net loss for the year you merely do not elect to bifurcate and keep your losses US side, thereby allowing yourself to book those losses and roll them over into future years (which is not allowed if the losses are PR-sourced).
There are separate rules for determining the bifurcation proportions for marketable vs. unmarketable securities. see pub 570 for details
To be clear, bifurcation is only able to be applied when:
- the assets are sold in a year in which you are a BFR-PR
- the assets are acquired before moving to PR
- the assets are certain types of investment property (for example, stocks, bonds, debt instruments, diamonds, and gold)
- For any of the 10 years preceding the year of the sale, you were a citizen or resident alien of the United States (other than a bona fide resident of the relevant territory).