Plutarch, Über die Geschwätzigkeit 11 (Moralia 508 A-B):

[...] But Fulvius (1), the friend of Caesar Augustus, heard the emperor, now an old man, lamenting the desolation of his house: two of his grandsons (2) were dead, and Postumius (3), the only one surviving, was in exile because of some false accusation, and thus he was forced to import his wife’s son (4) into the imperial succession; yet he pitied his grandson and was planning to recall him from abroad.

Fulvius divulged what he had heard to his own wife, and she to Livia; and Livia bitterly rebuked Caesar: if he had formed this design long ago, why did he not send for his grandson, instead of making her an object of enmity and strife to the successor to the empire.

Accordingly, when Fulvius came to him in the morning, as was his custom, and said, “Hail, Caesar [χαῖρε, Καῖσαρ],” Caesar replied, “Farewell, Fulvius [ὑγίαιν, Φούλβιε].” And Fulvius took his meaning and went away; going home a once, he sent for his wife, “Caesar has found out,” he said, “that I have not kept his secret, and therefore I intend to kill myself.”
“It is right you should,” said his wife, “since, after living with me for so long a time, you have not learned to guard against my incontinent tongue. But let me die first.” And, taking the sword, she dispatched herself before her husband.

(1) Fabius Maximus Fulvius
(2) Gaius und Lucius Caesar
(3) Agrippa Postumus
(4) Tiberius

Tacitus (Annalen I 5, 1 f.) berichtet die Geschichte erheblich anders, mit mehr Gift:

[...] Während man dies und ähnliches so dahinredete, verschlimmerte sich die Krankheit des Augustus, und manche argwöhnten eine Vergiftung durch seine Gattin. Denn das Gerücht hatte sich verbreitet, wenige Monate zuvor sei Augustus mit Wissen Auserwählter allein in Begleitung des Fabius Maximus nach Planasia gefahren, um Agrippa zu besuchen; viele Tränen dort auf beiden Seiten und Liebesbeteuerungen hätten die Hoffnung genährt, der junge Mann werde dem Haus des Großvaters wiedergegeben werden. Das habe Maximus seiner Frau Marcia erzählt, diese der Livia. Davon habe der Kaiser erfahren; und als nicht lange darauf Maximus starb, ungewiß ob nicht eines selbstgewählten Todes, habe man bei seiner Bestattung Marcias Seufzer gehört, die sich selbst anklagte, den Tod ihres Gatten verschuldet zu haben.