For which category of income does your client have a carryover?

Your client doesn't have to file a F.1116 for years no FTC is being claimed.  Carryover reported on F.1116 filed in a previous year will still be recognized.  You will still track that like you do with any other carryover in the workpaper for future reference.

If your client passes away prior to the carryover expiring, the last year it can be used would be the year your client is deceased.  By caselaw, carryovers generally die with the taxpayer since carryovers are attributable only to the taxpayer from whom they arose and aggregates between spouses are only allowed when joint filing election is in effect.