While real life is completely improvised, it takes exceptional talent to do it while being a fictional character. The best actors learned the art on their way up and continue to practice. Sometimes this results in pure magic. There are a lot of movies that include at least one scene improvised on the spot, but some rise above and become the one scene that people continually quote for years afterward. The newest ones we learn of is from The Dark Knight.
Heath Ledger owned the character of The Joker in Christopher Nolan’s 2008 Batman movie. Apparently Ledger, during his last role before he died, immersed himself in the crazed Gotham villain. Ledger improvised several times during the film including the jail scene where he sarcastically claps after Jim Gordon is promoted to Police Commissioner. However, the unscripted scene that truly shows Ledger’s dedication to the film and the character is when The Joker blows up the Gotham Hospital. With his madman makeup and wearing a nurse’s dress, The Joker exits the hospital while blowing it up. Apparently the explosions did not all go off as expected. The expensive scene was to be done in one take. Ledger stayed in character, looks perplexed, shrugs and fiddles with the bomb’s remote control until the explosions continued. That’s dedication to the character.
See five classic film scenes that were completely improvised at TVOM.
https://www.comicbookmovie.com/batman/what-everyone-gets-wrong-about-heath-ledgers-joker-the-dark-knight-a152301
Those are one-shot scenes. If he fell down, made a funny face, whatever, it would have to be kept and worked around, because you just can't do a massive building explosion more than once. I'd be curious to know if the director liked or disliked the change. Obviously it made a serious scene less serious, so it might actually have upset "the plan".