After a person pes away and you are their "executor", how would you know if an annuity exist?

You'd have to check her papers to see if there's any record of her ever paying an insurance company. Look through her checkbook. Check her bank statements to see if something was paid via automatic withdrawal. Check with her employer's HR department to see what work benefits she might have had. Have her incoming mail forwarded to you to see if she gets regular statements, quarterly perhaps. That's all you can do.