On Tuesday, Domenico Di Carlo and Massimo Ficcadenti both paid the price for their poor starts with Chievo and Cagliari respectively.
Palermo's Giuseppe Sannino had earlier been shown the door after taking just one point from his first three games, leaving Stroppa to count his blessings after delivering a worse return over the same period.
He told the Corriere dello Sport: "After three games and three defeats I was risking the sack, which would have seemed premature to me.
"But president (Daniele) Sebastiani put his faith in me and gave me the chance to carry on with this adventure.
"In Italy, coaches are often hired because they are fashionable at the time. It's not always about their methodology or what they've achieved on the pitch.
"The life of a coach is always a precarious one and that's why I'm happy to still be working with my team."
Stroppa might have followed Sannino, Di Carlo and Ficcadenti had he not swiftly turned the Delfini's form around to take seven points from the subsequent three games.
A third consecutive victory might be a bridge too far, though, given Pescara's lengthy list of absentees.
Suspensions for Vladimir Weiss and Damiano Zanon have not boosted Stroppa's hopes of conquering Lazio, with Uros Cosic, Francesco Modesto and Alessandro Crescenzi sidelined through injury.
Lazio have a more welcome selection problem, as head coach Vladimir Petkovic tries to fit Hernanes and Ederson into the same team.
The creative midfielders started together in a Europa League victory over Maribor and the Bosnian coach thinks there may be scope for a long-term working relationship.
"They did well, they played in different positions than they're used to," he told Gazzetta.it.
"Off the ball they were far apart and in possession they stuck together.
"But they were both key to the game and proved their value to the team."
The Biancocelesti were victorious when they last visited the Stadio Adriatico in 1992, a certain Paul Gascoigne getting among the goals.